Radar is widely used in aviation, meteorology and military fields, and radar pulse signal detection has become an indispensable and essential function of cognitive radio systems as well as electronic warfare systems. In this paper, we propose a deep learning based radar signal detection method. Firstly, we propose a detection method based on raw in-phase and quadrature (IQ) input, which utilizes a convolutional neural network (CNN) to automatically learn the features of radar pulse signals and noises, so as to accomplish the detection task. To further reduce the computational complexity, we also propose a hybrid detection method that combines compressed sensing (CS) and deep learning, which reduces the length of signal by compressed downsampling, and then feeds the compressed signal to the CNN for detection. Extensive simulation results show that our proposed IQ-based method outperforms the traditional short-time Fourier transform method as well as three existing deep learning-based detection methods in terms of probability of detection. Furthermore, our proposed IQ-CS-based method is able to achieve satisfactory detection performance with significantly reduced computational complexity.