The invention provides a periodic permanent-magnet focusing system capable of regulating magnetic field and a klystron. The periodic permanent-magnet focusing system comprises an electromagnetic coil adjustment device and a periodic permanent-magnet focusing device, wherein the electromagnetic coil adjustment device comprises N coils and a support shell, the N coils are arranged in an accommodating cavity of the support shell, and an outer-side coil pole shoe of the electromagnetic coil adjustment device is fixedly connected with one end of the periodic permanent-magnet focusing device. The electromagnetic coil adjustment device is arranged on a transition region of the klystron, so that an incident angle of an electron beam is matched with a periodic permanent-magnet focusing magnetic field, and the defect that the magnetic field of a traditional permanent-magnet focusing system cannot be regulated or is not convenient to regulate is overcome; a current value of the coil can be independently adjusted, the magnetic field is more flexible in regulation, and the regulation accuracy is higher; the klystron is provided with the periodic permanent-magnet focusing system and is high in beam quality; and the electromagnetic coil adjustment device is further arranged at the rear end of the periodic permanent-magnet focusing device, the transmission state of the electron beam can be adjusted, and relatively high electron beam transmission passing rate can be acquired.