A fine hole electrical discharge machine for machining a fine hole in a workpiece with the energy of electrical discharge generated by applying a voltage between an electrode for machining fine holes and the workpiece, the fine hole electrical discharge machine having an inclined electrode guide comprising: a main body in the form of a linearly extending member; a bendable guide tube having a hollow portion through which the electrode is inserted, the hollow portion having a larger inner diameter than an outer diameter of the electrode, wherein a proximal end-side of the guide tube is mounted to one side surface of the main body and is held substantially parallel to an axis; an inclined tube holder having a passage penetrating from a proximal end surface thereof to a distal end surface thereof, said inclined tube holder attaching a distal end of the guide tube to the main body, and supporting the distal end of the guide tube so as to incline the distal end-side of the guide tube at a desired angle, with respect to the axis, and characterized by: the inclined electrode guide further comprising a positioning guide mounted to a distal end of the inclined tube holder for guiding the electrode at a predetermined angle with respect to the axis; and an introducing member, arranged in the passage of the guide tube between the guide tube and the positioning guide, the introducing member being composed of a hollow member having an inner diameter which is tapered from an inlet thereof to an outlet thereof so as to guide the electrode from the guide tube to the positioning guide. a main body in the form of a linearly extending member; a bendable guide tube having a hollow portion through which the electrode is inserted, the hollow portion having a larger inner diameter than an outer diameter of the electrode, wherein a proximal end-side of the guide tube is mounted to one side surface of the main body and is held substantially parallel to an axis; an inclined tube holder having a passage penetrating from a proximal end surface thereof to a distal end surface thereof, said inclined tube holder attaching a distal end of the guide tube to the main body, and supporting the distal end of the guide tube so as to incline the distal end-side of the guide tube at a desired angle, with respect to the axis, and characterized by: the inclined electrode guide further comprising a positioning guide mounted to a distal end of the inclined tube holder for guiding the electrode at a predetermined angle with respect to the axis; and an introducing member, arranged in the passage of the guide tube between the guide tube and the positioning guide, the introducing member being composed of a hollow member having an inner diameter which is tapered from an inlet thereof to an outlet thereof so as to guide the electrode from the guide tube to the positioning guide. the inclined electrode guide further comprising a positioning guide mounted to a distal end of the inclined tube holder for guiding the electrode at a predetermined angle with respect to the axis; and an introducing member, arranged in the passage of the guide tube between the guide tube and the positioning guide, the introducing member being composed of a hollow member having an inner diameter which is tapered from an inlet thereof to an outlet thereof so as to guide the electrode from the guide tube to the positioning guide.