Hardware impairments can substantially limit the performance gain brought by the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). To address the above issue, this letter advocates a robust beamforming method for STAR-RIS in conjunction with the active beamforming at the base station for maximizing the sum-rate throughout the network. There are three main results. First, we extend the well-known weighted sum mean-square error minimization (WMMSE) method to the STAR-RIS beamforming with the hardware impairments taken into account. Then, the Schur’s complement and the first-order Taylor expansion are adopted to successively approximate the non-convex problem as a jointly convex problem of the amplitude and the phase variables. Furthermore, we propose a computationally efficient gradient projection method that optimizes the amplitude and phase alternately. Simulations demonstrate the effectiveness and robustness of the proposed algorithms in boosting the overall network throughput in the presence of hardware impairments.