Nonlinear process identification for control is studied. In identification test, the process is only tested (excited) along its operating-trajectory that includes various working points and transition periods. In model identification, a linear parameter varying (LPV) model is used. First linear models are identified using data sets at various working-points exclusive transition data; then the LPV model is identified by interpolating the linear models using total data. Sufficient conditions for a unique solution in parameter estimation will be given. Simulation study will be used to verify the effectiveness of the method. The identified model is suitable for model predictive control (MPC). 1