The computational complexity of the sparse reconstruction based on Direction of Arrival（DoA） increases with the search range of angle dramatically. To address this issue

this paper proposes a joint DoA estimation method based on Fast Fourier Transform（FFT） and sparse reconstruction.Firstly

the method solves the problem that the DoA estimation method based on the classical Fourier transform that can only estimate the direction of the incoming wave within half of the angular range.Then

the improved method can estimate the rough range of the incoming wave direction over the entire range of angles which can be used to roughly estimate the angle.Moreover

the sparse reconstruction method is used to perform super-resolution angle estimation in the range

which greatly reduces the range of angle search and reduces the computational complexity.Simulation results show that the proposed method can not only reduce the computational complexity

but also has less angular error at low signal-to-noise ratio and few snapshot.