A method of connecting a terminal fitting and an electric wire, includes the steps of: providing a terminal fitting; providing an electric wire in which a core wire is covered with an insulating sheath; providing a conductive connecting member formed with an insertion hole; inserting the electric wire into the insertion hole of the connecting member; compressing the connecting member radially inwardly so as to caulk an inserted portion of the electric wire uniformly over a whole periphery thereof; and welding the connecting member and the terminal fitting by applying ultrasonic wave.