Reconfigurable intelligent surface (RIS) has entered the public consciousness as a promising technology for enhancing the performance of future wireless communication systems by dynamically constructing the wireless channels. In this letter, we study a double-RIS aided downlink multi-user multiple-input multiple-output (MIMO) communication system. We investigate the mean-square-error (MSE) minimization problem by jointly optimizing the active transmit beamforming, the receive equalizer and the passive beamforming at each RIS. Different from prior works, for the sake of reducing both communication overhead and signal processing complexity, we assume that the two RISs utilize the common reflection pattern. Under this assumption, the coupling of the variables becomes tighter, thereby making the optimization problem more challenging to solve. To effectively address this issue, we propose a majorization-minimization (MM) based alternating optimization (AO) algorithm. Numerical results show that in high signal-to-noise ratio (SNR) region, the double-RIS with common reflection pattern can achieve nearly the same performance as that with separate reflection pattern whereas the complexity is only half of the latter. Thus, our proposed design enables an effective tradeoff between the performance and the implementation complexity of the considered system.