Electrical manipulation and read-out of quantum states in zero-dimensional nanostructures by nano-gap metal electrodes is expected to bring about innovation in quantum information processing. However, electrical tunability of the quantum states in zero-dimensional nanostructures is limited by the screening of gate electric fields. Here we demonstrate a new way to realize wide-range electrical modulation of quantum states of single self-assembled InAs quantum dots (QDs) with a liquid-gated electric-double-layer (EDL) transistor geometry. The efficiency of EDL gating is 6-90 times higher than that of the conventional solid gating. The quantized energy level spacing is modulated from ~15 to ~25 meV, and the electron g-factor is electrically tuned over a wide range. Such a field effect tuning can be explained by the modulation in the confinement potential of electrons in the QDs. The EDL gating on the QDs also provides potential compatibility with optical manipulation of single-electron charge/spin states.