A structure for coupling a faucet or a similar device includes: a faucet with a connecting pipe portion extending there-from; a connecting body with an annular coupling portion formed at one end and connected to a liquid supply source to discharge liquid through the faucet; a fastening nut screw-coupled to the annular coupling portion; a pressing ring coupled to the connecting pipe portion; and a grab ring configured to grab an outer circumference of the connecting pipe portion to have the connecting pipe portion not to be detached from the coupling portion. The fastening nut can be detached from the coupling portion by rotating the faucet and the connecting pipe portion with the engaging configurations of the pressing ring and the fastening nut in engaged position, and an angular position of the faucet can be adjusted to a preferred position in assembly by rotating the faucet and with the engaging configurations of the pressing ring and the fastening nut in disengaged position.