A simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided near-field multiple-input multiple-output (MIMO) communication framework is proposed. A weighted sum rate maximization problem for the joint optimization of the active beamforming at the base station (BS) and the transmission/reflection-coefficients (TRCs) at the STAR-RIS is formulated. The resulting non-convex problem is solved by the developed block coordinate descent (BCD)-based algorithm. Numerical results illustrate that the near-field beamforming for the STAR-RIS aided MIMO communications significantly improve the achieved weighted sum rate.