Abstract: In moving object recognition the features extracted are those insensitive to variations in the distance, position, illumination and projection of the moving ob-ject. The set of moments is insensitive or invariant to translation, rotation and scale change. So some supplementary features can be added to the set of moments to recognize moving object. Proves by theoretical deduction and experiment that the moment feature can be made robust and insensitive to translation, rotation and the illumination of environment with proper modifications. This is an important addition to the moment invariance theory applied to pattern recognition. In the last portion of the paper the proper range and experimental results are given to one set of formulas before modification and the other to one after modification respectively.