An internal gear pump that accommodates: a ring-shaped internally toothed gear provided with a plurality of internal teeth, and an externally toothed gear provided with a plurality of external teeth which internally mesh with the internal teeth of the internally toothed gear, the externally toothed gear being eccentrically disposed inside the internally toothed gear, the number of the plurality of internal teeth being one greater than the number of the plurality of external teeth, characterized in, that either in each one of the plurality of internal teeth, a tooth tip section and a meshing section are formed by a curve having one continuous curvature, the curve being formed by a curve having an X coordinate of Qx and a Y coordinate of Qy, Qx and Qy being provided by Equations to below with which a maximum curvature is at an apex of a tooth tip, and the curvature gradually reduces towards a tooth bottom, and that in each one of the plurality of external teeth, a tooth tip section, a meshing section and a tooth bottom section are formed by an envelope curve created by the curve forming the tooth tip section and the meshing section of the one of the plurality of internal teeth; or that in each one of the plurality of external teeth, a tooth tip section and a meshing section are formed by a curve having one continuous curvature, the curve being formed by a curve having an X coordinate of Qx and a Y coordinate of Qy, Qx and Qy being provided by Equation to below with which a maximum curvature is at an apex of a tooth tip, and the curvature gradually reduces towards a tooth bottom, and that in each one of the plurality of internal teeth, a tooth tip section, a meshing section, and a tooth bottom section are formed by an envelope curve created by the curve forming the tooth tip section and the meshing section of one of the plurality of external teeth; r = ro − dr ⋅ cos θ, Px = ro − dr + 1 / 4 dr 1 − cos 2 θ, Py = 1 / 4 dr − 2 θ + sin 2 θ, Qx = Px − r ⋅ cos θ, and Qy = Py + r ⋅ sin θ, where r is a radius of a curve, ro is a reference diameter, dr is a variation, where dr >0, θ is a parameter, Px is an X coordinate of a trajectory center, Py is a Y coordinate of the trajectory center, Qx is an X coordinate of a point on a curve generated by the trajectory center (Px, Py), and Qy is a Y coordinate of the point on the curve generated by the trajectory center (Px, Py). which internally mesh with the internal teeth of the internally toothed gear, the externally toothed gear being eccentrically disposed inside the internally toothed gear, the number of the plurality of internal teeth being one greater than the number of the plurality of external teeth, characterized in, that either in each one of the plurality of internal teeth, a tooth tip section and a meshing section are formed by a curve having one continuous curvature, the curve being formed by a curve having an X coordinate of Qx and a Y coordinate of Qy, Qx and Qy being provided by Equations to below with which a maximum curvature is at an apex of a tooth tip, and the curvature gradually reduces towards a tooth bottom, and that in each one of the plurality of external teeth, a tooth tip section, a meshing section and a tooth bottom section are formed by an envelope curve created by the curve forming the tooth tip section and the meshing section of the one of the plurality of internal teeth; or that in each one of the plurality of external teeth, a tooth tip section and a meshing section are formed by a curve having one continuous curvature, the curve being formed by a curve having an X coordinate of Qx and a Y coordinate of Qy, Qx and Qy being provided by Equation to below with which a maximum curvature is at an apex of a tooth tip, and the curvature gradually reduces towards a tooth bottom, and that in each one of the plurality of internal teeth, a tooth tip section, a meshing section, and a tooth bottom section are formed by an envelope curve created by the curve forming the tooth tip section and the meshing section of one of the plurality of external teeth; r = ro − dr ⋅ cos θ, Px = ro − dr + 1 / 4 dr 1 − cos 2 θ, Py = 1 / 4 dr − 2 θ + sin 2 θ, Qx = Px − r ⋅ cos θ, and Qy = Py + r ⋅ sin θ, where r is a radius of a curve, ro is a reference diameter, dr is a variation, where dr >0, θ is a parameter, Px is an X coordinate of a trajectory center, Py is a Y coordinate of the trajectory center, Qx is an X coordinate of a point on a curve generated by the trajectory center (Px, Py), and Qy is a Y coordinate of the point on the curve generated by the trajectory center (Px, Py). r is a radius of a curve, ro is a reference diameter, dr is a variation, where dr >0, θ is a parameter, Px is an X coordinate of a trajectory center, Py is a Y coordinate of the trajectory center, Qx is an X coordinate of a point on a curve generated by the trajectory center (Px, Py), and Qy is a Y coordinate of the point on the curve generated by the trajectory center (Px, Py).