<p><i>M</i>-tensor has important application value in practical problems, and eigenvalue is a crucial concept to study the properties of tensors. This paper presents an alternating minimization algorithm for the calculation of minimal H-eigenvalue of <i>M</i>-tensor. This algorithm decomposes the complicated tensor eigenvalue problem into two relatively simple subproblems, one is a least squared problem with a single variable, and the other is a multi-linear system problem. We study the convergence of the algorithm with numerical experiments, and illustrate the practicability and effectiveness of the algorithm compared with other algorithms by several numerical examples. </p>