The quantum Fourier transform(QFT)is a key subroutine of many quantum algorithms. NMR technology has been considered as one of the most effective physical system to realize quantum computation. QFT was introduced and drawn. After a further analysis,the quantum network which performs a multi-qubit QFT has been drawn out. Relevant unitary transforms of QFT were decomposed according to multiple-quantum operator algebra theory,and we designed the NMR pulse sequences to implement QFT. Finally,multi-qubit QFT was experimentally finished on a quantum computer emulator,which means the work we proposed is reasonable and practical.