This paper proposes a new hybrid maximum power point tracking (MPPT) algorithm combining grey wolf optimization (GWO) and perturb {\&} observe (P{\&}O) technique for efficient extraction of maximum power from a photovoltaic system subjected to rapid variation of solar irradiance and partial shading conditions. GWO handles the initial stages of MPPT followed by application of the P{\&}O algorithm at the final stage in view of achieving faster convergence to the global peak (GP). This MPPT thus overcomes the computational overhead as encountered in the case of a GWO-based MPPT algorithm reported earlier by Mohanty et al. The idea behind using the hybrid technique is to scale down the search space of GWO which helps to speed up for achieving convergence toward the GP. The proposed MPPT algorithm is first implemented using MATLAB/Simulink and subsequently an experimental setup is prepared for its practical implementation. From the obtained results, it is confirmed that the proposed MPPT provides superior tracking performance in any weather conditions compared to both GWO and PSO+PO-based MPPT algorithms.