Incorporating possible mechanisms in actual faults into the Olami-Feder-Christensen earthquake model(OFC model), we verified the results from the viewpoint of self-organizing critical phenomena. In the modelconsidering size, shape and static heterogeneity of the fault, the power law of the power index -1.2 is foundfor the energy (or scale) and the number of occurrences of the "earthquake", indicating that these resultswas not inherently affected by the parameter. However, considering attenuation and dynamicinhomogeneity, the absolute value of the exponent became large, but the power law was still observed.These results suggest that earthquakes based on the OFC model essentially represent self-organizedcritical phenomena. There were some cases where the statistical distribution of the temporal change of theearthquake energy could be approximated by the q-Gaussian distribution. Further research is required toclarify the criticality of the earthquakes in OFC model.