This letter investigates the joint design of transmit antenna selection (AS) and beamforming for downlink multiple-input-multiple-output (MIMO) networks, in which non-orthogonal multiple access (NOMA) transmission scheme is applied. We aim to maximize the achievable sum rate under the AS constraint and successful successive interference cancellation (SIC) constraints. The penalty dual decomposition (PDD) method coupled with the weighted mean squared error minimization (WMMSE) method is proposed to tackle this problem and a local optimal solution is obtained. Simulation results are provided to show the effectiveness of the proposed scheme.