An adaptive analytical Jacobian (AAJ) method has been developed by integrating the correlated dynamic adaptive chemistry and transport (CO-DACT) method with an analytical Jacobian method for efficient and stable chemical integrations. The CO-DACT method can produce locally reduced chemiscal kinetics on-the-fly with negligible computational cost even for a large chemical kinetic model. Based on the locally reduced chemical kinetics, the analytical Jacobian method with sparse matrix solver is applied to integrate the ordinary differential equation (ODE) system with a reduced Jacobian matrix. The performances of the proposed AAJ method are compared with a benchmarked hybrid multi-timescale (HMTS) method. The results show that the AAJ method is accurate and stable. It and can accelerate the overall computation with much larger integration time steps.