Speaker recognition systems are classified into Speaker Verification (SV) systems and Speaker Identification (SI) systems. A novel text-independent speaker identification system based on the Zak transform is implemented. The data used in this paper are drawn from the ELSDSR database. The efficiency of identification approaches 91.3% using a single test file and 100% using two test files. The paper shows comparable efficiency results with the well-known MFCC method with an advantage of being faster in both modeling and identification.