To reduce the radio krypton-85 concentration in liquid xenon, which is one of the commendable detecting media for dark matter detection, an efficient cryogenic distillation system to remove the krypton from the commercially available xenon was specifically designed, developed and constructed by using the McCabe-Thiele (M-T) method, mass conservation and energy conservation. The core of the distillation system is the packing tower which is 4 m high and 80 mm in diameter where a kind of efficient new structured packing PACK-13C was used. This distillation system can reduce the krypton in the xenon from 10-9 to 10-12 with 99% of Xe collection efficiency (i.e., the amount of Xe rejected is only 1%) at a maximum flow rate of 5 kg/h (15SLPM), which is crucial for the dark matter detector with a high-sensitivity and lowbackground.