Deep learning with its rapid development and advancement has achieved unparalleled performance in many areas like computer vision as well as cognitive radio and signal recognition. However, the performance of most deep neural networks would suffer from degradation in the data mismatch scenario, e.g., the test dataset has a related but nonidentical distribution with the training dataset. Considering the noise corruption, a classifier's accuracy might drop sharply when it is tested on a dataset with much lower signal-to-noise ratio compared to its training dataset. To address this dilemma, in this work we propose an efficient DeNoising and Classification Network (DNCNet) for radar signals. DNCNet consists of denoising and classification subnetworks. Firstly, a radar signal detection and synthetic mechanism is designed to generate pairwise clean data and noisy data for the DNCNet to train its denoising subnetwork. Then a two-phase training procedure is proposed to train the denoising subnetwork in the first phase and strengthen the mapping between the denoising results and perceptual representation in the second. Experiments on synthetic and benchmark datasets validate the excellent performance of the proposed DNCNet against state-of-the-art methods in terms of both signal restoration quality and classification accuracy.