A novel Adaptive Unified Predictive Control method (Adaptive-UPC) is proposed and applied to the first-order-plus-dead-time (FOPDT) process models with model uncertainties under unknown deterministic disturbances. Based on Indirect Self-tuning Regulator, this new control structure is constructed by combining UPC controller, Recursive Least-Squares Estimation with forgetting factor (RLS with forgetting factor) and Variable Regression Estimation (VRE). The simulation results show that the method can be effectively applied to first-order-plus-dead-time (FOPDT) process models with uncertain process parameters (gain, time constant and dead-time) and unknown deterministic disturbance.