Disclosed are a method of controlling a water injector for preventing damage to a catalyst for exhaust gas purification and an engine driven by the method. A method of controlling the operation of an injector for injecting water into the combustion chamber of an engine to which a turbo system for increasing the amount of air by compressing air has been applied includes a catalyst state determination step of determining the danger condition of a catalyst for exhaust gas purification by detecting the state of the catalyst, a water injection amount calculation step of calculating a water injection flow value F1 at which a temperature of exhaust gas drops to a preset temperature when the catalyst is in the danger condition, and a water injection step of performing the waterjet operation of a water injector based on the water injection flow value calculated in the water injection amount calculation step.