The cosmological origin of a large-scale gradient in the metallicity of the intra-cluster medium (ICM) discovered by ASCA has been examined. If the metal enrichment of the ICM completed before the gravitational collapse of the cluster, it is expected that the local galaxy-formation efficiency in the proto-cluster is imprinted as the local metallicity of the ICM. The galaxy-formation efficiency might be higher in the central region of the cluster than in its outskirts since the cluster-scale density fluctuation is higher and acts more efficient for pushing galaxy-scale density fluctuations up nearer to the cluster center. We extend the Press-Schechter theory to take into account the cluster environmental effects on the mass function of the virialized objects, derive an analytic formula to calculate the local galaxy-formation efficiency, and obtain the expected cosmological metallicity gradient in the ICM. Our results show, however, no significant metallicity gradient for our rich-nor poor-cluster models. On the otherhand, our canonical model for the XD cluster show a remarkable gradient in the metallicity distribution.