Signature as a personal attribute is one of the person's identity verification equipment that is accepted widely by the society. The process of signature recognition starts from starts from preprocessing, which consist of filtering, thresholding, thinning, cropping and resizing. After preprocessing continued by feature extraction process using Geometric Invariant Moment to get the value of a feature that will be used for the classification process using K-Nearest Neighbour. The variations Geometric Invariant Moment feature that has the smallest of FAR value and FRR value on each data source are different. For data from Indonesia the smallest FAR obtained while using moment 7 with value is 7% and the smallest FRR obtained while combining moment 1,2,3,6 and 7 and using all of the moment with each value is 61.5%. For data from Spain the smallest FAR obtained while combining moment 3,4,5 and 7, moment 1,3,4,5 and 7 and combining 1,3,4,5,6 and 7 with each value is 7% and the smallest FRR obtained while combining moment 2,3,4,5,6 and 7 and using all of the moment with each value is 72%. For data from Persia the smallest FAR obtained while combining moment 3 and 5 and combining moment 3,5 and 6 with each value is 9.5% and the the smallest FRR obtained while combining moment 1,2,3,4,6 and 7 with value is 37%. The testing results of FAR and FRR is inversely proportional. The system can recoginize the fake signatures well that proven by getting FAR value is relatively small on all of data sources. But the system can't recognize the original signatures well that proven by getting the high FRR value on all data sources. Features of Geometric Invariant Moment that applied globally on an image don't provide high accuracy. Perhaps, it happened because when apply global feature, the local features can't recognize properly. It occurs on the original signature image, while the application of the features of Geometric Invariant globally on the fake signature image provide high accuracy.