This letter considers temporal-correlated massive access, where each device, once activated, is likely to transmit continuously over several consecutive frames. Motivated by that the device activity at each frame is correlated to not only its previous frame but also its next frame, we propose a double-sided information (DSI) aided joint activity detection and channel estimation algorithm based on the approximate message passing (AMP) framework. The DSI is extracted from the estimation results in a sliding window that contains the target detection frame and its previous and next frames. The proposed algorithm demonstrates superior performance over the state-of-the-art methods.