Metal-oxide-semiconductor field-effect transistors (MOSFETs) using atomic-layer-deposited (ALD) Al$_2$O$_3$ as the gate dielectric are fabricated on the Si/Si$_{1-x}$Ge$_x$ heterostructures. The low-temperature carrier density of a two-dimensional electron system (2DES) in the strained Si quantum well can be controllably tuned from 2.5$times10^{11}$cm$^{-2}$ to 4.5$times10^{11}$cm$^{-2}$, virtually without any gate leakage current. Magnetotransport data show the homogeneous depletion of 2DES under gate biases. The characteristic of vertical modulation using ALD dielectric is shown to be better than that using Schottky barrier or the SiO$_2$ dielectric formed by plasma-enhanced chemical-vapor-deposition(PECVD).