Some existing low-rank approximation approaches either need to predefine the rank values (such as the matrix/tensor factorization-based methods) or fail to consider local information of data (e.g., spatial or spectral smooth structure). To overcome these drawbacks, this paper proposes a new model called the tensor nuclear norm-based low-rank approximation with total variation regularization (TLR-TV) for color and multispectral image denoising. TLR-TV uses the tensor nuclear norm to encode the global low-rank prior of tensor data and the total variation regularization to preserve the spatial-spectral continuity in a unified framework. Including the hyper total variation (HTV) and spatial-spectral total variation (SSTV), we propose two TLR-TV-based algorithms, namely TLR-HTV and TLR-SSTV. Using the alternating direction method of multiplier, we further propose two simple algorithms to solve TLR-HTV and TLR-SSTV. Extensive experiments on simulated and real-world noisy images demonstrate that the proposed TLR-HTV and TLR-SSTV outperform the state-of-the-art methods in color and multispectral image denoising in terms of quantitative and qualitative evaluations.