The non-local means (NLM) method is an effective and robust image denoising method. However, the existing NLM methods cannot guarantee the global optimum solution because they use a globally fixed bandwidth parameter when computing the similarity weight function. To address this problem, this article proposes an adaptive NLM method that can achieve a good trade-off between edge preservation and noise reduction. First, the difference curvature indicator is used to identify the local characteristics of each pixel. Then, depending on the properties of the difference curvature indicator, an adaptive bandwidth parameter is constructed. As a result, the bandwidth parameter depends continuously on the local characteristics of each pixel, which pixel-wise realize the selection of bandwidth. Experimental results show the effectiveness of our proposed method when compared with the mainstream methods.