In order to address the prediction uncertainty and control performance degradation caused by the long-term co-existence of connected and automated vehicles (CAVs) and human-driven vehicles (HDVs) in mixed traffic flow, a prediction-anchor-based model predictive control (PAMPC) method for platoon following is proposed. Historical trajectory information of the target HDV and surrounding vehicles is collected through roadside perception and vehicle-to-vehicle communication. Short-term future trajectories of the HDV are predicted by an attention-based long short-term memory (Attention-LSTM) network, and prediction anchors satisfying vehicle dynamic constraints are extracted from the predicted trajectories. The extracted prediction anchors are transformed into smooth ref-erence velocity information and incorporated into the cost function of a distributed MPC controller to facilitate the advance adjustment of control actions based on predicted behavioral trends while maintaining control smoothness. Simulation experiments are conducted based on the NGSIM dataset and the SUMO platform. The results indicate that, compared with a conventional MPC controller, the proposed method reduces the peak-to-peak acceleration of the platoon by approximately 50%, decreases the standard deviation of car-following distance by 42%, lowers inter-vehicle speed differences by 55%, and reduces passenger jerk under aggressive acceleration and deceleration disturbances. Furthermore, the applicability of the proposed method under non-ideal communication conditions is verified through packet-loss experiments, and its dependence on communication quality is revealed. In addition, it is demonstrated through weight sensitivity analysis that the controller maintains a certain degree of performance tolerance within a reasonable range of parameter perturbations. The results indicate that the proposed method provides a feasible approach for improving platoon-following performance and control smoothness in mixed traffic environments.