In this work, an offline signature identification system based on Histogram of Oriented Gradients (HOG) vector features is designed. Handwritten signature images are collected at Yildiz Technical University, from 15 people, 40 samples from each. Before the HOG feature extraction, size fixing and noise reduction processes are applied to all signature images. HOG features are extracted from the noiseless same sized images. In order to prevent the waste of processing time and to eliminate the redundant features, PCA is applied to the dataset. Obtained dataset is used to train the GRNN. As a result, a 98.33 percent test accuracy is obtained by using the proposed method along with two-folded cross correlation.