In this paper, Convolutional Neural Networks (CNN) are used to detect and classify micro-Doppler effects of maritime targets by using generalized learning ability for high-dimensional features. Based on the micro-motion model of maritime targets, two-dimensional time-frequency maps of four types of micro-motion signals are constructed in the measured sea clutter background. These maps were used as training and test datasets. Furthermore, three types of CNN models, i.e., LeNet, AlexNet, and GoogleNet, are used in binary detection and multiple micro-motion classifications. The effects of signal-to-noise ratio on detection and classification performance are also studied. Compared with the traditional support vector machine method, the proposed method can learn the micro-motion features intelligently, and has performed better in detection and classification. Thus, this study can provide a new technical approach for radar target detection and recognition under a cluttered background.