We present the mid-infrared (MIR) observation of a nearby galaxy cluster, A2255, by the AKARI space telescope. Using AKARI's continuous wavelength coverage between 3 and 24um and the wide field of view, we investigate the properties of cluster member galaxies to see how the infall of the galaxies, the cluster substructures, and the cluster-cluster merger influence their evolution. We show that the excess of MIR (~11um) flux is a good indicator for discriminating galaxies at different evolutionary stages and for dividing galaxies into three classes accordingly: strong MIR-excess (N3-S11>0.2) galaxies that include both unobscured and obscured star-forming galaxies; weak MIR-excess (-2.0<N3-S11<-1.2) galaxies that are quiescent, old (>5Gyr) galaxies where the MIR emission arises mainly from the circumstellar dust around AGB stars; and intermediate MIR-excess (-1.2<N3-S11<0.2) galaxies in between the two classes that are less than a few Gyr old past the prime star formation activity. With the MIR-excess diagnostics, we investigate how local and cluster-scale environments affect the individual galaxies. We derive the total star formation rate (SFR) and the specific SFR of A2255 using the strong MIR-excess galaxies.