In this paper, the convex optimal technique is applied to synthesis of sparse con- formal arrays for fitting the predefined patterns using as few elements as possible. The original synthesis problem can be formulated by minimizing the number of active elements subjected to the constraints on the pattern requirements. Unfortunately, it needs to solve a NP-hard problem since the objective function of the related problem is nonconvex. The minimization of the l1 -norm is presented to relax the above constraint into a convex way. Towards this end, the proposed method can determine both the corresponding locations and amplitudes of the sparse elements based on l1 -norm of the sparsest excitation set. The method for conformal array optimization addressed in this paper is easy to be implemented and has low computational load. Numerical simulations validate the effectiveness and high accuracy of the proposed synthesis method.