Detecting and classifying the modulation scheme of the intercepted noisy low probability of intercept (LPI) radar signals in real time is a necessary survival technique required in the electronic warfare systems. Therefore, LPI radar waveform recognition technique (LWRT) has gained an increasing attention recently. In this paper, we propose a convolutional neural network (CNN)-based LWRT, where the input and hyperparameters of the CNN, such as the input size, number of filters, filter size, and number of neurons are designed based on various signal conditions to guarantee the maximum classification performance. In addition, we propose a sample averaging technique to efficiently reduce the large computational cost required when the intercept receiver needs to process a large amount of signal samples to improve the detection sensitivity. We demonstrate the performance of the proposed LWRT with numerous Monte Carlo simulations based on the simulation conditions used in the recent LWRTs introduced in the literature. It is testified that the proposed LWRT offers significant improvement, such as robustness to noise and recognition accuracy, over the recent LWRTs.