The real-world tensor data are inevitably missing and corrupted with noise. Some models of the low-rank tensor factorization (LRTF) add an L1 norm or L2 norm to deal with the sparse or Gaussian noise. However, the real noise are usually complex. We propose a robust Bayesian tensor completion method, called MoG BTC-CP, which could impute the missing data and remove the complex noise simultaneously. The observed tensor is assumed to be the summation of a low-rank tensor and the noise. CP decomposition is proposed to extract the low-rank structure of the tensor. We assume that the noise follows a Mixture of Gaussian (MoG) distribution. A full Bayesian framework together with a Gibbs sampling algorithm is designed to estimate the model. Extensive experiments including synthetic data and real life applications show that MoG BTC-CP outperforms the recently published leading tensor completion and denoising methods. Copyright © 2022 Elsevier B.V. All rights reserved.