Abstract We study the problem of designing multicast precoders for multiple groups with the objective of minimizing total transmit power under certain guaranteed quality-of-service (QoS) requirements. To avail both spatial and frequency diversity, we consider a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. The problem of interest is in fact a nonconvex quadratically constrained quadratic program (QCQP) for which the prevailing semidefinite relaxation (SDR) technique is inefficient for at least two reasons. At first, the relaxed problem cannot be equivalently reformulated as a semidefinite programming (SDP). Secondly, even if the relaxed problem is solved, the so-called randomization procedure should be used to generate a high quality feasible solution to the original QCQP. However, such a randomization procedure is difficult in the considered system model. To overcome these shortcomings, we adopt successive convex approximation (SCA) framework in this paper to find beamformers directly. The proposed method not only avoids the randomization procedure mentioned above but also requires lower computational complexity compared to the SDR approach. Numerical experiments are carried out to demonstrate the effectiveness of the proposed algorithm.