The trip began at Cape Reinga on December 22, and has passed through Dargaville, Tauranga, Hamilton and New Plymouth so far. Journey's end is Bluff on February 4, with a record-breaking 3000km completed.
His previous longest roller ski was from Stockholm to Oslo in 2012, which came in at 2246km. It got him a short paragraph in the 2015 Guinness Book of Records.
Aged 28, Mr Baena loves both roller skiing and snow skiing. He once spent a winter at Wanaka, washing dishes five hours a day to finance his sport. On this trip he's hoping to meet Prime Minister John Key when he gets to Wellington.
"I really enjoy the movement, the adrenaline and the opportunity to represent my country and be a sports ambassador," he said.
He chose New Zealand for the record attempt because his grandmother always encouraged his skiing. They had planned to come here together - but she died recently.
"I promised her to cross New Zealand top to bottom. She never got the chance to visit here."
Venezuela has just one ski resort. But Mr Baena has been set on a ski career since he was 19. In his own country he has to roller ski at night when it's cooler, with lighted vehicles to support him.
His New Zealand trip is sponsored by Venezuela's Ministry of Sport, and equipment suppliers.