<p>In this paper, for repetitive discrete-time linear single-input single-output systems described by the state-space model, an iterative learning control algorithm with a tuning parameter is presented in order to utilize more historical control inputs and tracking errors. Necessary and sufficient conditions of the tuning parameter to guarantee the convergence of the tracking error are developed in terms of the spectral radius of an iterative matrix and the roots of a quadratic equation. Compared to some existing algorithms, the proposed control algorithm can improve the convergence speed of the tracking error by choosing a proper tuning parameter. Also, an explicit expression of the optimal parameter is derived to achieve the fastest convergence speed of the tracking error. Finally, the proposed theoretical results are validated by simulation.</p>