Learning an appropriate distance metric is a critical problem in pattern recognition. This paper addresses the problem in semi-supervised metric learning and proposes a new regularized semi-supervised metric learning (RSSML) method using local topology and triplet constraint. Our regularizer is designed and developed based on local topology, which is represented by local neighbors from the local smoothness, cluster (region density) and manifold information point of view. The regularizer is then combined with the large margin hinge loss on triplet constraint. We have implemented experiments on classification using UCI data set and KTH human action data set to evaluate the proposed method. Experimental results show that the proposed method outperforms state-of-the-art semi-supervised distance metric learning algorithms.