Many software systems provide users with a set of configuration options and different configurations may lead to different runtime performance of the system. As the combination of configurations could be exponential, it is difficult to exhaustively deploy and measure system performance under all possible configurations. Recently, several learning methods have been proposed to build a performance prediction model based on performance data collected from a small sample of configurations, and then use the model to predict system performance with a new configuration. In this paper, we propose a novel approach to model highly configurable software system using a deep feedforward neural network (FNN) combining with a sparsity regularization technique, e.g. the L_1 regularization. Besides, we also design a practical searching strategy for automatically tuning the network hyperparameters efficiently. Our method, called DeepPerf, can predict performance values of highly configurable software systems with binary and/or numeric configuration options at much higher prediction accuracy with less training data than the state-of-the art approaches. Experimental results on eleven public real-world datasets confirm the effectiveness of our approach.