In view of the challenges of non-Independent and Identically Distributed （non-IID） data and heterogeneous computing power faced in Federated Learning （FL） for edge computing applications， the concept of local drift variable was introduced to avoid the significant deviation in client model updates caused by non-IID data， thereby preventing unstable model convergence. By correcting the local model parameters， the local training process was separated from the global aggregation process， optimizing FL performance in non-IID data training process. Furthermore， considering the diversity of edge server computing power， a new strategy was proposed： a simplified neural network sub-model was divided from the global model for deployment on resource-constrained edge servers， while high-capacity servers utilized the complete global model. Parameters trained by the low-capacity servers were uploaded to the cloud server， with partial parameter freezing to accelerate model convergence. Integrating these two methods， a Federated learning optimization algorithm based on Local drift and Diversity computing power （FedLD） was proposed to solve the heterogeneous challenges caused by non-IID data and diversity computing power in FL for edge computing. Experimental results show that FedLD has faster convergence speed and higher accuracy compared to FedAvg， SCAFFOLD， and FedProx algorithms， compared to FedProx， when 50 clients are involved in training， FedLD improves the model accuracy by 0.39%， 3.68% and 15.24% on MNIST， CIFAR-10 and CIFAR-100 datasets， respectively. Comparative analysis with the latest FedProc algorithm reveals that FedLD has lower communication overhead. Additional experiments incorporating K-Nearest Neighbors （KNN） algorithm， Long Short-Term Memory （LSTM） model， and bidirectional Gated Recurrent Unit （GRU） model demonstrate approximately 1% accuracy improvements across all three models when integrated with FedLD.