This paper mainly concerns the problem of identifying a linear discrete time system with the aid of fractional order gradient method. At first, the fractional order gradient method is derived to guarantee the convergence to the extreme point. To avoid the singularity during the computing procedure, a modified fractional order gradient method is futher provided. On the basis of the proposed method, a novel method for identifying a linear discrete time system is presented, where the fractional order method shows a much faster convergence speed and higher convergence accuracy. Finally, some illustrative examples are provided to demonstrate the effectiveness of all the conclusions.