Frequency diverse array (FDA) can produce a range-angle-dependent beampattern due to the employment of a small frequency increment across the array elements. By utilizing this characteristic, this letter devises an FDA and multiple-input multiple-output hybrid radar to jointly estimate the ranges and angles of multiple targets via optimal transmit beamspace design. A uniform elemental power constraint is adopted as the optimization criterion is to minimize the mutual coherence of the sensing matrix using a sparse model and to achieve high-resolution estimation in both range and angle dimensions. A cyclic optimization approach based on power method-like is further developed to solve the non-convex design problem. The excellent performance of the proposed approach is demonstrated via computer simulations.