This work deals with a novel voltage sensorless based model predictive control (VSPC) scheme for continuous and quick maximum power harvesting (MPH) from photovoltaic (PV) array for solar-powered on-board EV (Electric Vehicle) charging system. In VSPC, the first model predictive control is used with a PV array to predict the system state in the horizon of time and to eliminate the voltage sensor. An adaptive concept is used for deciding the operating point, which accelerates the tracking process and improves dynamic performance during irradiation changes and shading pattern change in partial shaded condition. Moreover, VSPC also takes care of EV charging process using EV provided BMS (Battery Management System) command or threshold safety limits of the EV battery. The working principle of VSPC is based on a prediction of the future behavior of the system. It realizes on a selected time horizon, in an arbitrary number of samples, which is decided according to the complexity of the fitness function. In order to minimize or maximize the fitness function, it predicts the voltage of the solar PV array as well as tunes the present control signal, which forces it to converge or reach the convergence criteria. Moreover, cost and response time of current sensors are lower than voltage sensors. Therefore, the VSPC control gives a fast response and low power oscillations in steady-state compared to conventional techniques. This control technique is verified on a developed prototype of the PV system in different shading and irradiance conditions, as well as the system stability is analyzed through the Bode plot. The system performance is also compared with the state-of-the-art methods.