The applicant is SillaJen Biotherapeutics.
Pexa-Vec is a weakened virus that is based on a vaccine used in the eradication of smallpox.
The modified virus is injected into a cancer tumour in order to grow inside the rapidly growing cancer cells and kill them.
Overseas, more than 300 patients with advanced cancers have received Pexa-Vec treatments in previous clinical trials.
The EPA considers the benefits and risks of introducing new organisms, including GM organisms. This is done under the Hazardous Substances and New Organisms Act 1996 (the HSNO Act 1996).
The Act contains minimum standards which must be met before any release of a new organism can be considered.
EPA's general manager of applications and assessments, Sarah Gardner, said its decision was made after considering potential risks to the public's health and safety, valued species, natural habitats and the environment.
Controls will include restrictions on who can receive the virus, how it is administered, education of trial participants, and provision and collection of biohazard containers for waste.
SillaJen Biotherapeutics said in its application that Pexa-Vec was a promising therapy against liver cancer, with potential immediate benefits including tumour shrinkage, alleviation of symptoms, cancer remission and prolonged survival.
Phase 3 clinical trials involve a drug being given to large groups of people, potentially within public hospitals and clinical settings.
The use of GMOs is strongly opposed by some environmental groups and today's decision will be controversial.
Dr Nick Smith said there were some who wanted New Zealand to be completely GM-free.
"The Government's view is that a blanket ban on such technologies would deprive New Zealanders of biotechnologies like those for this potential liver cancer treatment.
"New Zealand is a country with strong environmental credentials but we are also a nation which has a rich scientific heritage. We should embrace new technologies like GM where there are clear benefits and where any risks to the environment can be effectively managed."
Dr Smith said New Zealand had "very cautious" laws around GMOs, but the country needed to be open to biotechnologies that offered real benefits and could save hundreds of lives.
"The Phase 3 clinical trial of Pexa-Vec is subject to tight controls that ensure the protection of the public and the environment. The next step for this trial is approval by Medsafe."
EPA assesses applications on a case by case basis.
In 2001, a Royal Commission on Genetic Modification was established to investigate issues surrounding genetic modification in New Zealand.
It recommended that New Zealand should proceed with caution while at the same time ensuring that any opportunities from genetic modification are preserved.
