Local scour around submerged square piles is very common in offshore and coastal engineering and can result in pile failure. In the study reported here, because the flow intensity (the ratio of the depth-averaged velocity to the threshold velocity for sediment particle motion) is one of the most important factors affecting the maximum scour depth in local scour, its effects on local scour around a submerged square pile was studied under clear-water scour conditions. A series of experimental tests with flow intensity in the range of 0.39-1.04 was conducted in steady current, and the flow intensity was classified as weak, transitional, or high according to the pattern of the scour hole upstream of the pile and the sand dunes downstream. The characteristics of sediment scour and deposition for temporal sediment bed elevation along a pile side and the temporal maximum scour depth were found to vary greatly among the three flow intensity conditions. An exponential function, which fitted the experimental data well, was used to fit how the maximum scour depth evolved, and the coefficients of time scale and scour depth proportion in the initial and development scouring stages were obtained at different values of the flow intensity.