In this article, a class of (alpha,beta )-metrics including Kropina metric are studied. They are called m-Kropina metrics and have the form F = alpha^{1-m}beta^m, (m ̸= 0, 1). When m = -1; it is Kropina metric F = alpha^2/beta . It is shown that, every m-Kropina metric with almost vanishing H-curvature has the vanishing H-curvature.
