Recent experimental advances in atomically thin transition metal dichalcogenide (TMD) metals have unveiled a range of interesting phenomena including the coexistence of charge-density-wave (CDW) order and superconductivity down to the monolayer limit. The atomic thickness of two-dimensional (2D) TMD metals also opens up the possibility for control of these electronic phase transitions by electrostatic gating. Here, we demonstrate reversible tuning of superconductivity and CDW order in model 2D TMD metal NbSe_{2} by an ionic liquid gate. A variation up to ∼50% in the superconducting transition temperature has been observed. Both superconductivity and CDW order can be strengthened (weakened) by increasing (reducing) the carrier density in 2D NbSe_{2}. The doping dependence of these phase transitions can be understood as driven by a varying electron-phonon coupling strength induced by the gate-modulated carrier density and the electronic density of states near the Fermi surface.