The company has faced a series of hurdles in launching its Electron rocket, known as Still Testing, into orbit.
Its inaugural test in May 2017 managed to reach space, but the rocket didn't make it into orbit after a communication fault forced the flight to be aborted early.
Shortly afterwards, Rocket Lab announced it would be suspending launch attempts until early 2018.
Sunday's launch is the first time a satellite has been launched into orbit from New Zealand.
Still Testing is carrying small Earth-imaging satellites for US companies Planet Labs and Spire Global.