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Geometric moment invariant (GMI) is well known approach in pattern recognition. One of the weaknesses of GMI is in its invarianceness, where data or points concentrated near to the center-of-mass are neglected because of the existence of data or points that are far away from the center-of-mass. To solve this problem, Balslev et.al has modified GMI method by adding a weighting function into GMIpsilas formula; thus we called it as Weighted Central Moment (WCM). WCM can increase noise tolerance for rotation/translation independent pattern recognition. In this paper, we present simulation results for characters with adjustable parameter alpha equal to 2/Rg. The experiments reveal that WCM yields intra-class results for identifying picture with different orientations. It also illustrates better inter-class distances in recognizing letter ldquogrdquo and ldquoqrdquo compared to GMI method.