Noise reduction is a very important task in image processing. In this aim, many approaches and methods have been developed and proposed in the literature. In this paper, we present a new restoration method for noisy images by minimizing the Total Variation (TV) under constraints using a multilayer neural network (MLP). Indeed, the obtained Euler-Lagrange functional is resolved by minimizing an error functional. The MLP parameters (weights) in this case are adjusted to minimize appropriate functional and provides optimal solution. The proposed method can restore degraded images and preserves the discontinuities. The effectiveness of our approach has been tested on synthetic and real images, and compared with known restoration methods