In mobile edge computing (MEC), load imbalance among edge servers occurs due to irrational task offloading strategies and resource allocation, as well as a sharp increase in the number of multi-type tasks. To address the above-mentioned issues, this study proposes a load prediction and balanced assignment scheme for multi-type tasks (LBMT) in a multi-user, multi-MEC edge environment. The LBMT scheme includes three components: task type classification, task load prediction, and task adaptive mapping. Firstly, considering the diversity of task types, a task type model is designed to classify tasks. Secondly, a task load prediction model is developed, considering the varying loads imposed by different tasks on servers, and employs an improved K-nearest neighbor (KNN) algorithm for load prediction. Thirdly, taking into account the heterogeneity of MEC servers and the limitation of resources, a task allocation model is designed in conjunction with a server load balancing model. Additionally, a task allocation method based on an adaptive task mapping algorithm is proposed. Finally, the LBMT scheme optimizes resource utilization and task processing rates for MEC servers to achieve the optimal load-balanced task offloading strategy. Simulation experiments compare LBMT with improved min-min offloading, intermediate node-based offloading, and weighted bipartite graph-based offloading schemes. The results show that LBMT improves the resource utilization rate by more than 12.5% and the task processing rate by more than 20.3%. Additionally, LBMT significantly reduces the standard deviation of load balancing, more effectively achieving load balance among servers.