In this paper, finite control-set model predictive control of two-level and three-level four-leg voltage source converters (VSCs) is presented. The predictive current control (PCC) and predictive voltage control (PVC) schemes are presented considering grid-connected and standalone distributed generation applications respectively. The discrete-time model of load currents, load voltages, DC-link capacitors voltage and VSC terminal voltages is formulated in terms of four-leg converter switching states. A cost function is defined with the PCC scheme to minimize the error between reference and predicted load currents. Similarly, in PVC scheme, the cost function deals with the minimization of error between reference and predicted load voltages. The balancing of split DC-link capacitors voltage is considered with the three-level four-leg VSCs. The optimal switching states which minimize the cost function are chosen and applied to the four-leg VSC directly without involving linear regulators and modulation stage. The proposed PCC and PVC strategies are verified through simulation results considering single-/three-phase, balanced/unbalanced and linear/nonlinear loads.