In computational drug discovery, accurately predicting drug-target interaction (DTI) is vital for drug repositioning and developing new drugs. With DTI data rapidly accumulated in recent years, it is recently hot to use deep learning technology to predict DTIs, but still a challenge to design light learning frameworks by using less protein descriptors. In this work, to address the challenge, a novel light deep convolutional neural network (namely LDCNN) is proposed to predict DTIs, in which a small number of protein descriptors are produced by convolving amino acid sequences of different lengths. As results, it is obtained that LDCNN can reduce the number of neurons in convolution layers and filters by 50%, with lose of AUC 1.3% and AUPR 4% comparing with DeepConv method. Our LDCNN models can give hints in designing light deep learning models for DTI prediction.