The invention discloses a process apparatus and method of nitrogen-containing natural gas dual-column cryogenic denitrification. The process apparatus comprises a denitrification cold box and a high-pressure denitrification column connected through a pipeline; a bottom outlet of the high-pressure denitrification column, the denitrification cold box and the high-pressure denitrification column areconnected in sequence; an upper outlet of the high-pressure denitrification column, a heat exchanger, the denitrification cold box and a low-pressure denitrification column are connected in sequence;a top outlet of the low-pressure denitrification column, the denitrification cold box, an ammonia compressor, a cooler, the denitrification cold box and a top feed port of the low-pressure denitrification column are connected in sequence; a bottom outlet of the low-pressure denitrification column, a fourth throttle valve, the denitrification cold box, a product gas compressor and the cooler are connected in sequence. Compared with the prior art, the process apparatus and method have the advantages the hydrocarbon content in nitrogen is greatly decreased, the purity of removed nitrogen is >/=99% by mol; cold is provided for the system after throttling of denitrified liquid hydrocarbon, external coolant circulation is canceled, and energy consumption of the apparatus is decreased.