A catheter guide wire is for use in guiding of a catheter to a destination position in vessels in body and comprises a solid core wire of a Ti-Ni shape memory alloy and an outer jacket covering the core wire. In order to provide a plasticity to one end portion of the core wire, at least one end portion is made of a 45.0-51.0 at % Ni-0.5-5.0 at % Fe-Ti shape memory alloy and is heat treated at 400.degree.-500.degree. C. The end portion is provided with a pseudo elasticity at a temperature about 37.degree. and a plasticity at a temperature below 80.degree. C. Alternatively, the end portion may be made of a 50.3-52.0 at % Ni-Ti alloy and is heat treated at a temperature of 700.degree. C. In order to improve operability of the catheter guide wire, the remaining portion other than the end portion is made of provided with a comparatively high rigidity by a usual Ti-Ni shape memory alloy which is not heat treated. Alternatively, the remaining portion is covered with an inorganic layer. The inorganic layer is a coating and alternatively is a cladding. The solid core wire is covered with a synthetic resin layer to form the catheter guide wire.