RCS reconstruction is an important way to reduce the measurement time in anechoic chambers and expand the radar original data, which can solve the problems of data scarcity and a high measurement cost. The greedy pursuit, convex relaxation, and sparse Bayesian learning-based sparse recovery methods can be used for parameter estimation. However, these sparse recovery methods either have problems in solving accuracy or selecting auxiliary parameters, or need to determine the probability distribution of noise in advance. To solve these problems, a non-parametric Sparse Iterative Covariance Estimation (SPICE) algorithm with global convergence property based on the sparse Geometrical Theory of Diffraction (GTD) model (GTD–SPICE) is employed for the first time for RCS reconstruction. Furthermore, an improved coarse-to-fine two-stage SPICE method (DE–GTD–SPICE) based on the Damped Exponential (DE) model and the GTD model (DE–GTD) is proposed to reduce the computational cost. Experimental results show that both the GTD–SPICE method and the DE–GTD–SPICE method are reliable and effective for RCS reconstruction. Specifically, the DE–GTD–SPICE method has a shorter computational time.