Abstract: Frequency diverse array (FDA) can produce a range-angle beampattern, but it has a range-angle coupling problem, which can usually be solved by designing nonlinear frequency increments or nonuniform spacing as well as producing a dot-shaped beampattern in the range-angle dimension. However, the conventional method of optimization is high in complexity. In this paper, we modify a mathematical model of beampattern for nonuniform FDA (sparse FDA). Based on the model, an approximately mathematical analysis of the mainlobe is given and a simplified objective function is proposed. After certain the optimal frequency increments and the constraints of the minimum element spacing, the genetic algorithm (GA) with the simplified objective function has been utilized to optimize the spacing of elements. The optimized sparse FDA has a thinner mainlobe both in the range and angle profile compared with the uniform FDA. Simulations verify the feasibility and efficiency of the proposed method.