The Russian Soyuz craft blasted off early on Saturday morning with one US astronaut and a Russian cosmonaut.
They will take over from the crew who have been on the ISS since November.
Columbia fell apart as it re-entered Earth's atmosphere on 1 February, killing all seven astronauts on board.
Before the disaster, there used to be two ways to get supplies and crew to the ISS.
Astronauts either used Nasa's shuttles or Russia's Soyuz craft.
The Soyuz is now the main way to get people up to the space station.
But Russian space officials are getting annoyed with the US because they say it is not helping enough with the cost of using just their spacecrafts.