The prior information of channel can't be induced in the process of channel estimation in MIMO relay communication system. To solve the problem, a novel semi-blind channel estimation based on variational inference is proposed. In this algorithm, some latent hyper-parameters such as factor precision, noise precision are introduced into the algorithm, and channel estimation probability model is built based on nested PARAFAC tensor decomposition. Since the posterior probability distribution of the channel parameters is complex, some point estimation methods, such as traditional maximum likelihood and maximum posteriori algorithm, are difficult to implement. The iteration formulas of factor matrix, factor precision and noise precision are deduced by the idea of variational inference principle, making the q distribution, which has the factor decomposition form, approach the unknown parameter posterior distribution. In addition, low bound of model evidence, model initiation and algorithm complexity are also analyzed. The algorithm can utilize the prior information of channel to improve channel estimation performance. The parameters can be tuned automatically, and complexity is linear with the dimension of observed data. Simulations show that the proposed algorithm has better estimation performance under flat Rayleigh channel condition, compared with No-blind algorithm, Alternating Least Square (ALS) based algorithm and No-linear Least Square (NLS) based algorithm, and has lower complexity and faster convergence speed, compared with alternating least square algorithm.