A high resolution range profile (HRRP) is a summation vector of the sub-echoes of the target scattering points acquired by a wide-band radar. Generally, HRRPs obtained in a non-cooperative complex electromagnetic environment are contaminated by strong noise. Effective pre-processing of the HRRP data can greatly improve the accuracy of target recognition. In this paper, a denoising and reconstruction method for HRRP is proposed based on a Modified Sparse Auto-Encoder, which is a representative non-linear model. To better reconstruct the HRRP, a sparse constraint is added to the proposed model and the sparse coefficient is calculated based on the intrinsic dimension of HRRP. The denoising of the HRRP is performed by adding random noise to the input HRRP data during the training process and fine-tuning the weight matrix through singular-value decomposition. The results of simulations showed that the proposed method can both reconstruct the signal with fidelity and suppress noise effectively, significantly outperforming other methods, especially in low Signal-to-Noise Ratio conditions.