The high resolution range profile （HRRP） of radar airborne targets is commonly used for target recognition. In practical operation， incomplete data samples and noise interference can present challenges to radar target recognition. To overcome this challenge， this paper combines stacked denoising auto-encoders （SDAE） with label constraints and convolutional neural networks （CNN） for HRRP denoising reconstruction and recognition. SDAE can denoise and reconstruct the HRRP data to enhance the data quality and expand the target dataset. By introducing label constraints in SDAE， the ability to associate the hidden features with the categories they belong to can be strengthened to accelerate the model convergence. The CNN is used to classify the HRRP. Experimental results show that the proposed method in this paper demonstrates superior recognition performance in target recognition under small samples and strong noise scenarios， and is able to overcome the adverse effects of fewer samples and higher noise on HRRP recognition to a certain extent.