An injection system of an injection molding machine and an injection molding machine. The injection system of an injection molding machine comprises a screw (1); a transmission shaft (10), the transmission shaft (10) comprising a ball spline section and a ball screw section, or the transmission shaft (10) comprising a ball spline section and a planetary roller screw section; and a nut mechanism and an axial guide mechanism (11). The injection molding machine comprises the injection system and a mold closing system. When the injection system and the injection molding machine perform an injection action, except the screw (1) and the transmission shaft (10), there are few components required to move, i.e., other driving and transmission components do not make axial motion along the injection action. During an injection action, the system has a light mass and the motion inertia is decreased, such that the response speed and precision of the injection action is improved, and the driving efficiency is reduced.