Federated Learning (FL) is a novel distributed machine learning paradigm that addresses privacy concerns while training the robust model across distributed clients. The primary challenge of FL is the heterogeneity of data distribution, which slows down model convergence and degrades model performance. Especially, constrained by computational capacity and network bandwidth in edge computing applications, FL client optimization methods have become crucial for addressing the issue of the heterogeneity of data. Nevertheless, existing approaches overlook the impact of local training overfitting, which degrades the global model performance. Additionally, they fail to fully take advantage of the existing local model on clients. In this work, we propose a novel and lightweight client optimization method. Specifically, we utilize the gradient variate with the client historical offset computed by the local model and updated global model to guide the local objective function. Moreover, we provide a strategy that randomly adds gradient perturbations during training to prevent the local objective function from converging to local optima. Extensive experiments demonstrate that, under various heterogeneity scenarios, our proposal exhibits strong competitiveness compared to current state-of-the-art client optimization algorithms, with notable improvements in both performance and robustness.