The adaptive Kriging method is widely used in the engineering design for complex black-box problems, yet its accuracy is limited by imbalanced exploitation–exploration. This paper proposes a KNN-based maximization of the weighted expected prediction error (KMWEPE) method to address this challenge. For each iteration, the most sensitive region is identified by the leave-one-out cross-validation error (LOOCVE) and the distance between sample points. Two different sets of candidate points are generated, respectively, in the most sensitive region and the design space, in order to dynamically balance the local exploitation and global exploration. Then, the bias–variance decomposition method is used to convert the expected prediction error of each candidate point into the sum of the bias and the Kriging prediction variance. And the bias is replaced by the weighted sum of the LOOCVE of the K-nearest neighbors sample points based on KNN. Furthermore, the arithmetic sum of the bias and the Kriging prediction variance above is used to construct a new function. Finally, the candidate with the maximum weighted expected prediction error is selected as the new sample point for the next iteration. Six benchmark test functions, two publicly available datasets, and two engineering examples are tested to demonstrate the effectiveness of the proposed KMWEPE method in improving the model accuracy. The test results show that compared to the LHD and MEPE methods, the RMSE mean and standard deviation of the KMWEPE method decreased by an average of 31.6% and 28.8%, respectively.