I have heard of nuclear propulsion, however I wonder that is it possible for it to launch into space, and if so, how much fuel would it need?
The NERVA was a fairly heavy engine, with a thrust to weight ratio of about 3:1 in flight configuration (as compared to ratios of better than 100 for liquid-fueled engines). Between that and the fact that its exhaust included radioactive material, it wouldn't have been a good choice for a lower-stage engine, but it would have been possible. Improved nuclear-thermal engine designs like Project Timberwind could have achieved 30:1 TWR, but the cost and environmental issues would still make it a poor choice for a first stage.
Fuel efficiency of a nuclear-thermal engine is about twice as good as a hydrogen-oxygen combustion rocket, so you'd need only half as much fuel mass as your hydrogen-oxygen-fueled competition as a rule of thumb, but the fines from the EPA would easily wipe out any cost savings.