A pipe-fitting device capable of easily connecting pipes having different diameters includes a fitting body and a pair of fixing nuts. The fitting body includes a first channel portion having a first inner diameter formed in a first inner side of the fitting body, a second channel portion having a second inner diameter formed in a second inner side of the fitting body, the second inner diameter being smaller than the first inner diameter such that a step is formed inside the fitting body at the boundary between the first channel portion and the second channel portion. Each fixing nut is rotatably coupled to a corresponding open end of the fitting body and configured to fix the corresponding one of the first pipe and the second pipe through rotational tightening.