In this article, first we compute H-curvature of (α,β)-metrics, when β is a closed 1-form. Next, we apply this formula to discuss some special (α,β)-metrics and we obtain necessary and sufficient conditions for these metrics to have almost vanishing H-curvature. Moreover we characterize Einstein square metric F = (α+β)^2/α , when β is a closed 1-form and in this case it is proven that it has vanishing H-curvature.
