The continuous integration of cloud computing and mobile Internet promotes the generation and development of mobile cloud computing (MCC), but it is difficult to meet the demand for bandwidth and delay of terminal applications. Mobile edge computing (MEC) provides computing and storage capabilities at the edge of the user's network. By computing offloading, the terminal task is migrated to the edge server for execution, which can effectively reduce application delay and conserve terminal energy consumption. However, this has certain limitations in practical applications for existing works that focus on a single mobile terminal and assume the server's resources are sufficient for task offloading on MEC environment. This study focuses on the task offloading problem under the resource-constrained MEC environment and proposes a multi-user serial task dynamic offloading strategy (MSTDOS). The strategy uses the completion time of the application and the energy consumption of the mobile terminal as evaluation indicators, follows the principle of first come first served, uses a chemical reaction optimization algorithm to solve, while can make a near-optimal offloading strategy for the application by consider the interactionamong multiple terminals and dynamically adjust the selection decision. Simulation results show that MSTDOS strategy can achieve better application performance than existing algorithms.