As an emerging decentralized machine learning technique, federated learning organizes collaborative training and preserves the privacy and security of participants. However, untrustworthy devices, typically Byzantine attackers, pose a significant challenge to federated learning since they can upload malicious parameters to corrupt the global model. To defend against such attacks, we propose a novel robust aggregation method-maximum correntropy aggregation (MCA), which applies the maximum correntropy criterion (MCC) to derive a central value from parameters. Different from the previous use of MCC for denoising, we utilize it as a similarity metric to measure parameter distribution and aggregate a robust center. Correntropy in MCC, with all even-order moments of the parameter, contains high-order statistical properties, which allows for a comprehensive capture of parameter characteristics, thus helping to prevent interference from attackers. Meanwhile, correntropy extracts information from the parameters themselves, without requiring the proportion of malicious attackers. Through the fixed-point iteration, we solve the optimization objective, demonstrating the linear convergence of the iteration formula. Theoretical analysis reveals the robustness aggregation property of MCA and the error bound between MCA and the global optimal solution, with linear convergence to the optimal solution neighborhood. By performing independent identically distribution (IID) and non-IID experiments on three different datasets, we show that MCA exhibits significant robustness under mainstream attacks, whereas other methods cannot withstand all of them.