The natural ventilation of buildings can be achieved effectively with solar chimneys, which are classified into wall, roof, and combined wall–roof configurations. Among the combined systems investigated in the literature, vertical wall–horizontal roof solar chimneys have not been evaluated thoroughly. This study investigates the performance of a combined vertical wall–horizontal roof solar chimney numerically. A two-dimensional Computational Fluid Dynamics (CFD) model is employed to examine the flow and thermal characteristics under various influencing factors relating to the chimney’s geometry, the flow resistance caused by the bend connecting the vertical and horizontal portions, the reverse flow at the outlet, and the location of the heat source. Compared to a vertical wall chimney at the same cavity height, the combined system always had a lower flow rate but had a higher thermal efficiency at some length-to-total-height ratios. Heating the upper walls induced higher flow rates but lower thermal efficiency. Particularly, the effect of the bend on the flow rate was more important than that of the reverse flow at the outlet. These results imply that a combined chimney is preferred over a vertical one for heating applications, wherein the combined chimney should have transparent upper walls.