A high-dimensional sparse signal usually should be realigned as a long 1D signal to be recovered by orthogonal matching pursuit (OMP), an efficient algorithm for compressed sensing. Clearly, however, the realigned long signal will result in a large amount of computation in OMP. If each atom in the dictionary can be expressed as the Kronecker product of two vectors, it can possible to decompose this dictionary into two sub-dictionaries. By exploiting this property, a fast OMP algorithm for 2D sparse signals of this kind is presented, and applied to 2D angle estimation in MIMO radar. Simulation results verify its good reconstruction quality approximate to that of OMP and greatly improved computational efficiency.