Handcraft features are commonly used for signal classification, which is a time-consuming feature engineering. In order to develop a general and robust feature learning method for radio signals, a novel One-dimensional Deep Attention Convolution Network (ODACN) is proposed to automatically extract discriminative features and classify various kinds of signals. First, one-dimensional (1-D) sparse filters are designed to learn hierarchical features of raw signals. Second, an attention layer is constructed to weight and assemble feature maps, to derive more context-relevant representation. By using simple 1-D filtering, ODACN is characteristic of less parameters and lower computation complexity than traditional Convolutional Neural Networks (CNNs). Moreover, feature attention can mimic a succession of partial glimpses of humans and focus on context parts of signals, thus helps in recognizing signals even at low Signal-to-Noise Ratio (SNR). Some experiments are taken to classify 31 kinds of signals with different modulation and channel coding types, and the results show that ODACN can achieve accurate classification of very similar signals, without any prior knowledge and manual operation.