$\mathcal{H}$-tensors play an important role in the stability study of automatic control systems, polynomial optimization problems, medical image de-noising problems, and so on. But it is not easy to determine whether a given tensor is an $\mathcal{H}$-tensor or not in practice. In this paper, we give some practical criteria for $\mathcal{H}$-tensors by constructing different positive diagonal matrices and applying some techniques of inequalities. As an application, some sufficient conditions for the positive definiteness of an even-order real symmetric tensor are given. Advantages of obtained results are illustrated by numerical examples.