The alleged breaches are also "representative of CLSAP NZ's general approach to compliance with its obligations" under the AML/CFT over that time, the FMA claimed.
The FMA's claim, which was filed in Auckland, is seeking a pecuniary penalty against CLSAP NZ and costs.
The maximum penalty for such alleged breaches is $2m for a company.
The directors of CLSAP NZ during the time of the alleged breaches were Rongjun (June) Zhang, Songyuan Huang (Benny Wong), Stefan Liu, Robert Manwarring Noakes and Richard Clive Pearson. The directors are not parties to the proceedings, the FMA said.
FMA general counsel Nick Kynoch said New Zealand's anti-money laundering legislation, which was introduced a decade ago, is a cornerstone to protecting the integrity of the country's financial system.
"It's imperative that financial services firms ensure they are compliant.
"The regime has been in place since 2013 and CLSAP's alleged breaches are serious so it is appropriate for the FMA to take a strong regulatory response. CLSAP NZ needs to be held to account and our approach sends an important message of deterrence to the industry."
Last year's trial of Jiaxin Finance, its sole director Qiang Fu and his mum and employee Fuqin Che was the first case of its kind in New Zealand's courts since specific anti-money laundering laws were introduced.
The Auckland firm and the mother and son pair were found guilty of failing to keep adequate records for and report 311 suspicious transactions, worth $53.4m.
The company was fined $2.55m, while Che was fined $202,000 and Fu hit with a $180,000 personal penalty in March by Justice Tracey Walker.
The $53.4m belonged to Chinese-Canadian mogul Xiao Hua Gong, also known as Edward, who is accused of running a $200m pyramid scheme.
Gong also has nearly $70m in Kiwi assets currently restrained, which are anticipated to be part of what will be a record civil forfeiture application by police.