To mitigate the inter-cell interference in multicell downlink systems, this letter consider the robust precoder design for multicell cooperation where the knowledge of channel state available at the base station is imperfect. Assuming that imperfect channel state information (CSI) can be exchanged among cells but with no data sharing, we investigate the worst-case performance optimization problem with bounded CSI error. Our objective is to minimize the weighted sum mean-square-error (MSE) subject to per-base-station power constraints. A distributed solution is obtained by reformulating the upper bound of MSE and exploiting the Lagrangian method for the optimal problem. Simulation results demonstrate that the proposed algorithm is robust to guarantee the worst-case sum rate performance and has lower computational complexity than the SINR-based design.