Chandrayaan-2 was launched at 14:43 local time (09:13 GMT) from the Sriharikota space station.
The spacecraft is carrying an orbiter, a lander and a rover that will move around on the lunar surface for 14 earth days. It will take around 47 days to travel before landing on the moon.
India’s space chief said his agency had “bounced back with flying colours” after the aborted first attempt.
The spacecraft has entered the Earth’s orbit, where it will stay for 23 days before it begins a series of manoeuvres that will take it into lunar orbit.
If successful, India will become the fourth country to make a soft landing on the Moon’s surface. Only the former Soviet Union, the US and China have been able to do so.