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Sr_{2}IrO_{4} was predicted to be a high-temperature superconductor upon electron doping since it highly resembles the cuprates in crystal structure, electronic structure, and magnetic coupling constants. Here, we report a scanning tunneling microscopy/spectroscopy (STM/STS) study of Sr_{2}IrO_{4} with surface electron doping by depositing potassium (K) atoms. We find that as the electron doping increases, the system gradually evolves from an insulating state to a normal metallic state, via a pseudogaplike phase, and a phase with a sharp, V-shaped low-energy gap with about 95% loss of density of state (DOS) at E_{F}. At certain K coverage (0.5–0.6 monolayer), the magnitude of the low-energy gap is 25–30 meV, and it closes at around 50 K. Our observations show that the electron-doped Sr_{2}IrO_{4} remarkably resembles hole-doped cuprate superconductors.