It is a key problem to constrain the minimum interelement spacing in the sparse antenna array synthesis. A perturbed compressive sampling (PCS) and a convex optimization are two existing sparse array synthesis methods, which have their shortcomings of small spacing between adjacent elements when solving practical problems. In this letter, a new method for sparse planar array synthesis with the interelement minimum spacing constraint is proposed by combining the advantages of PCS and convex optimizations. This method solves the problems of small spacing in PCS synthesize results and long solving time or even invalid for the large-scale array in the convex optimization methods. Moreover, the method can ensure that the gain of the sparse array is similar to the uniform counterpart. The numerical results show that the method can maintain the merits of sparsity, peak sidelobe level, and gain while constraining the minimum interelement spacing.