Many recent deep learning platforms rely on third-party libraries (such as cuBLAS) to utilize the computing power of modern hardware accelerators (such as GPUs). However, we observe that they may achieve suboptimal performance because the library functions are not used appropriately. In this paper, we target at optimizing the operations of multiplying a matrix with the transpose of another matrix (referred to as NT operation hereafter), which contribute about half of the training time of fully connected deep neural networks. Rather than directly calling the library function, we propose a supervised learning based algorithm selection approach named MTNN, which uses a gradient boosted decision tree to select one from two alternative NT implementations intelligently: (1) calling the cuBLAS library function; (2) calling our proposed algorithm TNN that uses an efficient out-of-place matrix transpose. We evaluate the performance of MTNN on two modern GPUs: NVIDIA GTX 1080 and NVIDIA Titan X Pascal. MTNN can achieve 96\% of prediction accuracy with very low computational overhead, which results in an average of 54\% performance improvement on a range of NT operations. To further evaluate the impact of MTNN on the training process of deep neural networks, we have integrated MTNN into a popular deep learning platform Caffe. Our experimental results show that the revised Caffe can outperform the original one by an average of 28\%. Both MTNN and the revised Caffe are open-source.