In this paper, we propose a new approach to cover song identification using a CNN (convolutional neural network). Most previous studies extract the feature vectors that characterize the cover song relation from a pair of songs and used it to compute the (dis)similarity between the two songs. Based on the observation that there is a meaningful pattern between cover songs and that this can be learned, we have reformulated the cover song identification problem in a machine learning framework. To do this, we first build the CNN using as an input a cross-similarity matrix generated from a pair of songs. We then construct the data set composed of cover song pairs and non-cover song pairs, which are used as positive and negative training samples, respectively. The trained CNN outputs the probability of being in the cover song relation given a cross-similarity matrix generated from any two pieces of music and identifies the cover song by ranking on the probability. Experimental results show that the proposed algorithm achieves performance better than or comparable to the state-of-the-art.