Nonsingular $H$-matrix is a special class of matrices which has wide applications in computational mathematics, matrix theory, economic mathematics and control theory. In this paper, according to the special properties of $M$-matrices and $\gamma$-chain diagonally dominant matrices, and constructing positive diagonal matrices and subdividing the index set of matrices, we obtain several new conditions for judging $H$-matrices by applying some special inequalities and inequality techniques. The criteria extend some of the recent results, and the numerical examples illustrate the effectiveness of the theoretical results.