A roll-and-press friction-driving harmonic drive gear reducer includes: a wave generator having an elliptical external contour; a flexible spline having an output end and an open annular wall connected to the output end, the open annular wall having an external circumferential surface that includes an external roll-and-press area in an annular form, the external roll-and-press area including an annular section of external teeth adjacent to an end edge and a circumferential external curved surface adjacent to the annular external teeth; and a circular spline, which has an end that is recessed to form an accommodation hole that is inwardly extended, the accommodation hole having an internal circumferential surface that includes an internal roll-and-press area, the internal roll-and-press area including an annular section of internal teeth adjacent to an end edge and a circumferential internal curved surface adjacent to the set of internal teeth.