In this paper, a generalized Hammerstein model consisting of a static polynomial function in series with time-varying linear model is proposed in order to model the Hammerstein-like multivariable processes whose linear dynamics vary over the operating space. An iteration procedure is proposed to identify the generalized Hammerstein model by using the just-in-time learning (JITL) technique. Unlike the conventional Hammerstein model, only the static nonlinear part of generalized Hammerstein model, thus identified is retained in its subsequent application in controller design. Consequently, the on-line use of proposed model requires the identification of linear model by using the JITL technique and current process data. An adaptive decentralized PID control strategy based on the proposed model is also developed. The controller parameters are adjusted on-line by using the gradient descent algorithm and information provided by the JITL. Simulation results show that the proposed methods have better prediction accuracy and control performance than those achieved by the conventional Hammerstein model and its associated adaptive decentralized PID controller design, respectively.