This paper presents a maximum power point tracking (MPPT) method using model predictive technique for a grid-tied photovoltaic harvesting energy system. A single-stage grid-tied Z-source inverter is used for extracting the maximum available power and feeding the power to the grid. The proposed technique predicts the future behavior of the photovoltaic side voltage and current by using a digital observer which estimates the parameters of the photovoltaic module. The proposed method features simultaneously reduction in oscillation around maximum power point (MPP) and fast convergence by adaptively changing the perturbation size using the predicted model of the system. The experimental results demonstrate fast tracking response under dynamic weather condition, small steady state error, small oscillation around MPP at steady state, and high MPPT efficacy for wide range of solar irradiance levels. Additionally, the grid side current total harmonics distortion (THD) meets the IEEE-519 standards.