In recent years, the triplet loss-based deep neural networks (DNN) are widely used in the task of face recognition and achieve the state-of-the-art performance. However, the complexity of training the triplet loss-based DNN is significantly high due to the difficulty in generating high-quality training samples. In this paper, we propose a novel DNN training framework to accelerate the training process of the triplet loss-based DNN and meanwhile to improve the performance of face recognition. More specifically, the proposed framework contains two stages: 1) The DNN initialization. A deep architecture based on the softmax loss function is designed to initialize the DNN. 2) The adaptive fine-tuning. Based on the trained model, a set of high-quality triplet samples is generated and used to fine-tune the network, where an adaptive triplet loss function is introduced to improve the discriminative ability of DNN. Experimental results show that, the model obtained by the proposed DNN training framework achieves 97.3% accuracy on the LFW benchmark with low training complexity, which verifies the efficiency and effectiveness of the proposed framework.