LPI radar signal recognition based on convolutional neural networks usually assumes that the signal to be recognized belongs to a closed set of known signal classes. In an open electromagnetic signal environment, this type of closed-set recognition method will experience a drastic drop in performance due to the encounter with unknown types of signals. We propose an SCNN-SVDD model based on a combination of a lightweight convolutional neural network and a support vector data description algorithm to achieve open-set recognition of LPI radar signals under unknown signal conditions. In this approach, Choi-William's time-frequency distribution is used to obtain two-dimensional time-frequency images of the signal to be identified, and convolutional neural networks are used to achieve high-precision classification of known signals and extract the corresponding feature vectors. Then, the feature vectors are used as input to the SVDD algorithm and a hypersphere is constructed to detect whether the signal to be identified belongs to a known class. Experimental results show that the proposed method can detect unknown signals while maintaining high recognition accuracy for known signals.