In this paper，it mainly discussed the fixed point properties of the mean non-expansive mapping．First of all，it proved the weakly compact convex subset with Opial properties for mean non-expansive mapping that has weak fixed point property． Secondly，it discussed the weakly compact convex subset of reflexive Banach space X which has asymptotic normal structure that has a fixed point for mean non-expansive mapping Finally，it proved that when the Garcia-Falset constant satisfied specific inequality，the mean non-expansive mapping T has a fixed point.