Abstract: Based on the conformal mapping, Green function method was applied in hexagonal geometry. Conformal mapping was used to map a hexagonal node to a rectangular node before transverse integration. Then, the transverse integration equations were resolved using Green function method with the second boundary condition. A three-dimensional multi-energy-groups static program NACK was programmed based on those theories. The code was verified by VVER-1000-type core without the reflector, VVER-440-type three-dimensional two-energy-groups core and two-dimensional core with discontinuity factors. The eigenvalue error is less than 50 pcm, and the maximum relative error of the node average power is less than 2%. The accuracy of NACK is as good as that of other advanced node method codes.