Monolayers of transition-metal dichalcogenides (TMDs) exhibit numerous crystal phases with distinct structures, symmetries and physical properties. Exploring the physics of transitions between these different structural phases in two dimensions may provide a means of switching material properties, with implications for potential applications. Structural phase transitions in TMDs have so far been induced by thermal or chemical means; purely electrostatic control over crystal phases through electrostatic doping was recently proposed, but has not yet been realized. Here we report first experimental demonstration that electrostatic doping could drive phase transition between the hexagonal and monoclinic phases of monolayer molybdenum ditelluride (MoTe2). Such transition is accompanied with hysteresis measured in Raman and Second Harmonic Generation. Polarization-resolved spectroscopies reveal crystal orientation before and after phase transition. It potentially bridges unique properties in monolayer materials such as valley degree of freedom, Ising pairing and topological transport. Such an unprecedented electrostatic driven structural phase transition opens new door for applications like electronic memory and low power switching.