Abstract: This paper proposes a new-type periodical permanent magnet (PPM) focus system, each half period of which is composed of 1 magnetic pole and 5 permanent magnets, and the first, the third and the fifth magnets have reverse magnetization with the second and the fourth magnets. Besides, any two magnets spaced half period have inverse magnetization with each other. The new-type PPM focus system is modeled and calculated by MTSS2018, the results show that the axial component B_z of the magnetic induction intensity on the axis has conspicuous amplitude of the third and the fifth space harmonics, and B_z rises steeply after it reaches zero, so B_z has a profile very approximate to the periodical rectangular shape. An electron gun under the condition of the above calculated B_z is calculated by MTSS2018 too, a beam with 22 kV of voltage, 215 mA current and 0.08 mm of maximum beam radius is obtained, which meets the demand of G band extended interaction klystron (EIK). In the calculations the peak value of B_z is only 1.2 \sqrt 2 B_B (subscript B is Brillouin magnetic field), it suggests that the new-type PPM focus system focuses the beam effectively even if it has a relatively lower peak value of B_z than the conventional PPM focus system does.