K-nearest neighbor (KNN) rule is a simple and effective classifier in pattern recognition. In this paper, we propose a new nearest neighbor classifier based on multi-harmonic mean distances, in order to overcome the sensitivity of the neighborhood size k and improve the classification performance. The proposed method is called a harmonic mean distance-based k-nearest neighbor classifier (HMDKNN). It mainly designs the multi-harmonic mean distances based on the multi-local mean vectors calculated by utilizing k nearest neighbors of the given query sample in each class. Using the multi-harmonic mean distances per class, a new nested harmonic mean distance in each class is designed as the classification decision and the query sample is classified into the class with the closest nested harmonic mean distance among all classes. The experimental results on the UCI data sets show that the proposed HMDKNN performs better with the less sensitiveness to k, compared to the state-of-art KNN-based methods.