In this paper, we consider transmit beamforming to multiple multicasting groups. We assume that the different multicasting groups share the same frequency band and that the channel state information (CSI) in terms of either instantaneous channels or the second order channel statistics is available at the transmitter. For the problem of maximizing the minimum signal-to-interference-plus-noise ratio (SINR) of all the receivers under a total power constraint, a sequential convex programming algorithm is developed. Compared to the method proposed in the literature, the developed algorithm achieves a higher SINR at a significantly reduced computational complexity.