The present invention belongs to the technical field of air sterilizing and purification and in particular relates to a plasma air sterilizing and purifying device and an air sterilizing and purifying method. The plasma air sterilizing and purifying device comprises a plasma reactor, a pulse power supply, a fan component, a control device, a power adaptor, and a housing case, wherein the reactor is provided with positive electrodes formed by several nickel-chromium alloy wires or nickel-chromium alloy belts, and the two ends of each positive electrodes are fixed in the corresponding grooves on the micro-discharge preventive conductor rail; and a pulse power supply has a digital control circuit with an oscillator, an error amplifier and a PWM comparator inside which converts signals into a digital control current to control the width of the high-voltage pulse.