Abstract: By Hall’s marriage theorem, we study lower bounds of the Lin-Lu-Yau curvature of amply regular graphs with girth 3 or 4 under different parameter restrictions.As a consequence,we show that each conference graph has positive Lin-Lu-Yau curvature.Our approach also provides a geometric proof of a known diameter estimates of amply regular graphs in the case of girth 4 and some special cases of girth 3.