An off-shore wind turbine resting on the sea bottom, the wind turbine comprising: • a base having a bottom bearing surface bearing against the ground of the sea bottom once in place; and • a pylon supported by said base, the bottom end of the pylon preferably being fixed in embedded manner in said base; and • a wind engine supported by said pylon at its top end and comprising a rotary shaft of horizontal axis driven in rotation by an engine and supporting a plurality of blades with said wind engine being coupled to an electricity generator, the generator preferably likewise being supported by said pylon at its top end; and • said base includes a tubular cavity of axis (Z 1 Z' 1) that is preferably perpendicular to said bottom bearing surface of the base, a bottom portion of said pylon being fixed inside said tubular cavity, the fixing being performed by means of a device for adjusting the angle of inclination of the axis (ZZ') of said pylon (3, 6) to be adjusted relative to the axis (Z 1 Z' 1) of said tubular cavity; said device for adjusting the angle of inclination of said pylon in said base comprising: a) independent chocking means interposed between said pylon bottom portion and said tubular cavity at the level (BB') of the top opening of said tubular cavity projecting above sea level once in place; and b) centering means (6-3, 6-4) secured to said pylon bottom portion and to said tubular cavity, said centering means being situated inside said tubular cavity beneath said chocking means, and said centering means comprising a first centering element secured to a bottom wall of said tubular cavity, located at the center thereof and co-operating with a second centering element located at the center of the bottom end of said pylon bottom portion, said centering means being suitable for holding the point of intersection between the axis (ZZ') of said pylon bottom portion and the axis (Z 1 Z' 1) of said tubular cavity in a fixed position at the bottom of said tubular cavity. • a base having a bottom bearing surface bearing against the ground of the sea bottom once in place; and • a pylon supported by said base, the bottom end of the pylon preferably being fixed in embedded manner in said base; and • a wind engine supported by said pylon at its top end and comprising a rotary shaft of horizontal axis driven in rotation by an engine and supporting a plurality of blades with said wind engine being coupled to an electricity generator, the generator preferably likewise being supported by said pylon at its top end; and • said base includes a tubular cavity of axis (Z 1 Z' 1) that is preferably perpendicular to said bottom bearing surface of the base, a bottom portion of said pylon being fixed inside said tubular cavity, the fixing being performed by means of a device for adjusting the angle of inclination of the axis (ZZ') of said pylon (3, 6) to be adjusted relative to the axis (Z 1 Z' 1) of said tubular cavity; a) independent chocking means interposed between said pylon bottom portion and said tubular cavity at the level (BB') of the top opening of said tubular cavity projecting above sea level once in place; and b) centering means (6-3, 6-4) secured to said pylon bottom portion and to said tubular cavity, said centering means being situated inside said tubular cavity beneath said chocking means, and said centering means comprising a first centering element secured to a bottom wall of said tubular cavity, located at the center thereof and co-operating with a second centering element located at the center of the bottom end of said pylon bottom portion, said centering means being suitable for holding the point of intersection between the axis (ZZ') of said pylon bottom portion and the axis (Z 1 Z' 1) of said tubular cavity in a fixed position at the bottom of said tubular cavity.