An extrusion blow molding machine comprises an extrusion apparatus, an electrically-driven parison thickness programming apparatus, an electrically-driven mold-clamping apparatus with a dual-driving function, and a frame, wherein the extrusion apparatus, the parison thickness programming apparatus and the mold-clamping apparatus with a dual-driving function are installed on the frame. The mold-clamping apparatus with a dual-driving function comprises a driving assembly, a mold-opening/closing assembly, a mold-moving assembly, and a base. The driving assembly includes a servo motor, which actuates both mold-opening/closing and mold-moving assemblies, respectively. The parison thickness programming apparatus is driven by asynchronous motors, which run in a single direction continuously to result in a required axial parison thickness distribution. An extrusion blow molding method is realized using the machine. The present extrusion blow molding machine has an obviously simplified and compact structure, thereby reducing the manufacturing cost, lowering the energy consumption, and improving the transmission efficiency and position accuracy.