This paper proposed an image denoising technique that can enhance the quality of image by using a variational approach and image gradient distribution. First, in order to remove the noise, we consider the variational approach for the energy functional that satisfies an edge-preserving regularization property. Here, we propose a new variational functional that can be implemented by adding a new gradient distribution term in a given energy functional that locally controls the extent of denoising over image regions according to their gradient magnitudes. And by using the fundamental lemma for the calculus of variations, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a devised functional. Next, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Through various experiments, we can demonstrate that the proposed method can preserve the edges while removing noise better than existing techniques.