Sparse models have been widely used in image denoising, and have achieved state-of-the-art performance in past years. Dictionary learning and sparse code estimation are the two key issues for sparse models. When a dictionary is learned, sparse code estimation is equivalent to a general least absolute shrinkage and selection operator (LASSO) problem. However, there are two limitations of LASSO: 1). LASSO gives rise to a biased estimation. 2). LASSO cannot select highly correlated features simultaneously. In recent years, methods for dictionary construction based on the nonlocal self-similarity property and weighted sparse model, relying on noise estimation, have been proposed. These methods can reduce the biased gap of the estimation, and thus achieve promising results for image denoising. In this paper, we propose an elastic net with adaptive weight for image denoising. Our proposed model can achieve nearly unbiased estimation and select highly correlated features. Experimental results show that our proposed method outperforms other state-of-the-art image denoising methods.