A method of brazing a pipe member to a counterpart member includes steps of mounting in a circumferential direction an engaging portion in a ring shape to an outer periphery of the pipe end portion proximate an endmost portion of the pipe member, engaging a brazing-filler-metal-made ring in a ring shape with the engaging portion, inserting the pipe end portion of the pipe member provided with the brazing-filler-metal-made ring into the counterpart member, heating and melting the brazing-filler-metal-made rug with the outer peripheral surface of the pipe end portion being in abutment with the inner peripheral surface of the counterpart member, pouring a brazing filler metal into an abutment portion between the outer peripheral surface of the pipe end portion and the inner peripheral surface of the counterpart member, and securing by brazing the pipe end portion to the counterpart member.