Adaptive control systems are designed to achieve desired control performance when plant parameters gains are unknown, or possibly slowly changing. Highly calculation technology is developed, more important discrete-time adaptive control structure is. Because the relative degree condition for strict positive realness (SPR) of the discrete-time error transfer function is different from the condition of the continuous time case, it is hard to prove the stability of the discretized continuous-time adaptive control systems. The main contribution of this paper is the extension of an Immersion and Invariance (I&I)-based adaptive control algorithm from continuous to discrete time. The theoretical stability of the proposed discrete time I&I-based adaptive control system is proved. In order to show the effectivaness of the proposed method, numerical simultions are shown.