The design of sparse array which is able to achieve good performance of beam-pattern satisfying the minimum peak sidelobe level (PSL) with the number of sensors as few as possible is a research area of increasing interest. This paper presents a method for planar optimization with sensor selection via convex optimization in condition of constrained beam-pattern. In the optimization procedure, the solution algorithm is based on convex optimization including a reweighted l1-norm minimization. The objective is the minimum of the number of sensors and the PSL. Sparse array is obtained by removing those sensors with weights equal to zero or approximately equal to zero. In this paper, we also give the optimization algorithm respectively by row, column and the intersection on the basis of the linear array optimization. Numerical results are included, which illustrate the optimum method for planar arrays overall performs better than the other methods presented above for sensor selection.