With regard to inverse synthetic aperture radar imaging with limited bandwidth and sparse aperture, it is a challenge to traditional range-Doppler (RD) algorithm. We proposed an innovative two-dimensional (2D) joint sparse imaging algorithm, namely, 2D fast orthogonal matching pursuit (2D-FOMP) algorithm. In the proposed algorithm, one-dimensional OMP (1D-OMP) is extended to 2D-OMP in the complex domain from three aspects of atom recognition, projection update, and residual update. Then, the equivalence between 1D-OMP and 2D-OMP is analyzed theoretically. Meanwhile, two strategies that multi atom recognition and matrix recursive update are added in 2D-OMP to further improve the reconstruction speed of 2D-FOMP. Experimental results based on both simulated and measured data demonstrate that the proposed algorithm has good imaging performance under noisy and sparse conditions.