The temporal variation of local pier scour depth is very complex, especially for cases where the bed comprises a sediment mixture. Many semi-empirical models have been proposed to predict the time-dependent local pier scour depth. In this paper, an alternative approach, the support vector regression method (SVR) is used to estimate the temporal variation of pier-scour depth with non-uniform sediments under clear-water conditions. Based on dimensional analyses, the temporal variation of scour depth was modeled as a function of seven dimensionless input parameters, namely flow shallowness (y/Dp), sediment coarseness (Dp/d50), densimetric Froude number (Fd), the difference between the actual and critical densimetric Froude number (Fd − Fdβ), geometric standard deviation of the sediment particle size distribution (σg), pier Froude number (U/gDp) and one of the following three dimensionless time scales (T1 = t/tR1, T2 = t/tR2 and T3 = t/tR3). The SVR model not only estimates the time-dependent scour depth more accurately than conventional regression models, but also provides results that are consistent with the physics of the scouring process.