The predominant topology to connect the Photovoltaic (PV) system to the grid is the two-stage conversion process integrated with PI-based controllers. In the last decade, single-stage conversion has drawn significant attention due to relatively low conversion losses and installation costs. Operating a single stage grid connected PV system using the model predictive control (MPC) method is introduced in the literature very recently. Under such a scheme, the behaviours of the different maximum power point algorithms are still unknown. This paper investigates the performance of swarm-based Maximum Power Point Tracking (MPPT) techniques in MPC controlled single-stage grid-connected PV systems. For comparison, three algorithms namely particle swarm optimization, grey wolf optimization and artificial bee colony are chosen. All MPPT algorithms are cascaded with a continuous control set-based model predictive controller for inverter control. MPPT schemes are tested under uniform irradiance variation and partial shading conditions. It is observed that in a 12S30P PV configuration, an artificial bee colony performs slower tracking compared to the other two. Nevertheless, all three algorithms track the global MPP under all conditions successfully. The swarm-based MPPT techniques perform well with the MPC controller and a smooth AC signal is generated for grid integration. The total harmonic distortion (THD) is recorded as 3.05% in the steady state.