This letter introduces a non-local means (NLM) denoising algorithm that uses a weight function based on a switching norm. The noise level and local activity are incorporated into the NLM denoising algorithm which enhances performance. This is done by selecting a norm among l₁, l₂, and l₄ norms to determine a weighting function. The experimental results show the capability of the proposed algorithm. In addition, the proposed algorithm is verified as effective for enhancing the performance of other NLM algorithms.