A radio-frequency and baseband hybrid beamforming (HBF) scheme is presented for spatial division multiple access (SDMA) of 60GHz applications using planar antenna arrays (PAA). PAA with phase shifters for each element antenna is partitioned into sub-blocks and each block is applied a common baseband beamforming weight. To suppress the grating lobes of beam pattern and to maintain the signal to interference plus noise ratio (SINR) of users in the SDMA system, we study the design of this HBF using convex optimization. Two design criteria are considered herein: one minimizes the transmit power subject to a SINR constraint, and the other maximizes the worst case SINR subject to a total power constraint. Simulation results show that both the SINR and directivity of HBF can be significantly improved by making use of the convex optimization technique.