We discuss the electron mobility (µ) of a two-dimensional electron gas (2DEG) confined at the MgxZn1-xO/ZnO heterointerface grown by molecular-beam epitaxy. With increasing x from 0.05 to 0.2, the electron density (n) was enhanced and µ was suppressed due to interface roughness or alloy disorder scattering. By the optimization of growth conditions, in particular growth rate, ionized impurity scattering in the ZnO channel could be reduced significantly. With tuning n by a gate voltage on top-gated Hall-bar devices, the peak µ at 2 K was enhanced to 130,000 cm2 V-1 s-1 at n = 3×1011 cm-2.