In this paper, the Matsumoto metric with special Ricci tensor has been investigated. It is proved that, if F is of positive (negative) sectional curvature and F is of alpha -parallel Ricci curvature with constant killing 1-form, then (M,F) is a Riemannian Einstein space. In fact, we generalize the Riemannian result established by Akbar-Zadeh.
