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This paper presents the findings from the laboratory wave flume experiments designed to investigate the formation and evolution of scour around a non-slender, square vertical structure, under three flow conditions, solitary wave, combined solitary wave and steady following current, and combined solitary wave and steady opposing current. The structure was placed on a sandy berm, either fastened to the flume wall or positioned at the centerline of the flume. For the wave only case, the scour on the seaside edge turned out to be deeper than the one on the leeside regardless of the structure’s position. The analyses showed that the depth, width, volume, and location of the scour were all significantly influenced by the introduction of steady currents. The following current, for example, deepened the seaside scour, while leading to shallower leeside scour holes as a result of the backfilling process. Contrary to the opposing current, which shifted the scour area in the upwave direction, the scour was transported downwave under the effect of the following current. The scour depth was determined to be a function of the structure position and the Keulegan-Carpenter number, whereas the scour width mostly depended on the structure’s position. In this regard, the structure fastened to the wall experienced the widest scour area and the largest volume regardless of the flow condition.