The electromagnetic scattering problem over a wide incident angle can be rapidly solved by introducing the compressive sensing theory into the method of moments, whose main computational complexity is comprised of two parts: a few calculations of matrix equations and the recovery of original induced currents. To further improve the method, a novel construction scheme of measurement matrix is proposed in this paper. With help of the measurement matrix, one can obtain a sparse sensing matrix, and consequently the computational cost for recovery can be reduced by at least half. The scheme is described in detail, the analysis of computational complexity and numerical experiments are provided to demonstrate the effectiveness.