It is the country where Cecil the lion was killed, sparking international anger against the American dentist who shot him.
The outcry over Walter Palmer's killing of Cecil drove other big-game hunters away from Zimbabwe, fearful they too would attract the opprobrium of the public.
But in what is being described as a side-effect of the affair, Zimbabwe's largest wildlife area says it now finds itself suffering from an overpopulation of lions.
Bubye Valley Conservancy has more than 500 lions, the largest number in Zimbabwe's diminishing wildlife areas.
It has warned that its lion population has become unsustainable and that it may even have to cull around 200 as a result of what is being called "the Cecil effect".
Now Bubye is appealing for other institutions or wildlife sanctuaries to take some of its lions.
Conservationists estimate about half of Zimbabwe's wildlife has disappeared since president Robert Mugabe's seizure of white-owned land began in 2000, but Bubye has held on by attracting wealthy hunters whose fees support its wildlife work.
But last year's shooting of Cecil, in a conservancy bordering Hwange National Park, sparked a huge backlash against big-game hunting, and bolstered a US plan to ban trophy hunting imports.
Plummeting oil prices have further led to a drop in the number of visitors from US states such as Texas, from where traditionally large numbers of hunters go to Zimbabwe.
Bubye's lions are decimating populations of antelope, along with other animals such as giraffe, cheetah, leopards and wild dogs, after the driest summer on record kept grasses low and made the small game easy targets.
Blondie Leathem, general manager of Bubye Valley Conservancy, said: "I wish we could give about 200 of our lions away to ease the overpopulation. If anyone knows of a suitable habitat for them where they will not land up in human conflict, or in wildlife areas where they will not be beaten up because of existing prides, please let us know and help us raise the money to move them."
In the Forties, there were thought to be as many as 450,000 lions on Earth, but today they are classed as "vulnerable", with numbers feared as low as 20,000.
Conservationists fear that without a concerted push, particularly in high-risk areas of central and west Africa, their numbers could halve again in the next two decades because of human-animal conflict and reduced habit and food supplies.
Bubye, along with some game parks in neighbouring countries, has been bucking the trend, according to a recent study, with healthy lion populations in "small, fenced, intensively managed, funded reserves". The conservation area was founded 22 years ago by Charles Davy, the rancher father of Chelsy Davy, Prince Harry's former girlfriend. It is now majority-owned by Dubai World, the investment fund of the wealthy emirate's government.
Millions of pounds were spent fencing 2,000 square miles of land previously cleared of wildlife by decades of cattle farming. The fence was then electrified and hundreds of people were hired to protect wildlife imported to the park.
Bubye also supports schools and clinics in several districts and provides meat every month for people nearby.
As well as its lion population, Bubye also has the third-largest community of black rhinos in Africa.
When The Sunday Telegraph visited Bubye in early February a matriarch lioness called Matilda, her sisters and her latest litter of cubs were lazing in the shade under mopane trees.
Matilda - who was fitted with a radio collar by the Oxford University researchers that also collared Cecil - chews through at least 10lb of meat every day.
Peter Kay, director of Lion Aid, a UK-based charity, said contraception should have been introduced at the conservancy years ago. "It's too late now," he said. "There is nowhere in Africa which could take so many lions."
Paul Bartels, a wildlife scientist from South Africa's Tshwane University of Technology, said female contraceptive implants used in smaller reserves would be impractical for Matilda's clan.
"There are a lot of lions on that [Bubye] conservancy. It would cost hundreds of thousands of dollars for contraception to make any real difference," he said.
Oxford's lion research project in Zimbabwe, which monitored Cecil, said that the Bubye conservancy was "a huge success story" in a region blighted by a lack of governmental help for its struggling wildlife sector.
Mr Leathem insisted he was not a hunter but a conservationist, and had no option but to maintain "sustainable" hunting to safeguard Bubye's future.