Efficient distribution of service requests between fog and cloud nodes considering user mobility and fog nodes’ overload is an important issue of fog computing. This paper proposes a heuristic method for task placement considering the mobility of users, aiming to serve a higher number of requested services and minimize their response time. This method introduces a formula to overload prediction based on the entry-exit ratio of users and the estimated time required to perform current requests that are waiting in the queue of a fog node. Then, it provides a solution to avoid the predicted overloading of fog nodes by sending all delay-tolerant requests in the overloaded fog node’s queue to the cloud to reduce the time required for servicing delay-sensitive requests and to increase their acceptance rate. In addition, to prevent requests from being rejected when the mobile user leaves the coverage area of the current fog node, the requests in the current fog node’s queue will be transferred to the destination fog node. Simulation results indicate that the proposed method is effective in avoiding the overloading of the fog nodes and outperforms the existing methods in terms of response time and acceptance rate.