The quality of a multichannel audio signal may be reduced by missing data, which must be recovered before use. The data sets of multichannel audio can be quite large and have more than two axes of variation, such as channel, frame, and feature. To recover missing audio data, we propose a low-rank tensor completion method that is a high-order generalization of matrix completion. First, a multichannel audio signal with missing data is modeled by a three-order tensor. Next, tensor completion is formulated as a convex optimi-zation problem by defining the trace norm of the tensor, and then an augmented Lagrange multiplier method is used for solving the con-strained optimization problem. Finally, the missing data is replaced by altating itera-tion with a tensor computation. Experiments were conducted to evaluate the effectiveness on data of a 5.1-channel audio signal. The results show that the proposed method out-performs state-of-the-art methods. Moreover, subjective listening tests with MUSHRA (Multiple Stimuli with Hidden Reference and Anchor) indicate that better audio effects were obtained by tensor completion.