This paper studies the temporal-correlated massive access system where a large number of devices communicate with the base station sporadically and continue transmitting data in the adjacent frames in high probability when being active. By exploiting the sparsity and the temporal correlations of the user activities, the joint user activity detection and channel estimation (JUADCE) problem in multiple consecutive frames can be formulated as a dynamic compressed sensing (DCS) problem. Specifically, we formulate a probabilistic model that accounts the statistics of channels and characterizes the evolutions of the user activities by a steady Markov chain. The hybrid generalized approximate message passing (HyGAMP) framework is leveraged to develop a computationally efficient algorithm named HyGAMP-DCS to solve the JUADCE problem. The HyGAMP-DCS algorithm performs channel estimation in the GAMP part and soft user activity information update in the MP part, then exchanges intrinsic information between these two parts for performance enhancement. Simulation results demonstrate that the proposed algorithm can significantly outperform the conventional DCS-based algorithms and the GAMP algorithm which ignores the temporal correlations.