Building a system to identify individuals through their speech recording can find its application in diverse areas, such as telephone shopping, voice mail and security control. However, building such systems is a tricky task because of the vast range of differences in the human voice. Thus, selecting strong features becomes very crucial for the recognition system. Therefore, a speaker recognition system based on new spin-image descriptors (SISR) is proposed in this paper. In the proposed system, circular windows (spins) are extracted from the frequency domain of the spectrogram image of the sound, and then a run length matrix is built for each spin, to work as a base for feature extraction tasks. Five different descriptors are generated from the run length matrix within each spin and the final feature vector is then used to populate a deep belief network for classification purpose. The proposed SISR system is evaluated using the English language Speech Database for Speaker Recognition (ELSDSR) database. The experimental results were achieved with 96.46 accuracy; showing that the proposed SISR system outperforms those reported in the related current research work in terms of recognition accuracy.