The ANC-H code is the hexagonal geometry version of the Westinghouse three-dimensional advanced nodal code ANC. Together with PHOENIX-H, the hexagonal geometry version of the Westinghouse pressurized water reactor (PWR) lattice code PHOENIX-P, they provide the Westinghouse code package for designing VVER-type PWR cores of hexagonal geometry. The nodal theory of ANC-H is the net current nodal expansion method implemented with the technique of conformal mapping, which maps a hexagon to a rectangle while preserving the diffusion operator. The use of conformal mapping eliminates the root cause of singularities resulting from the conventional transverse integration. The intranode burnup gradient is accounted for by allowing spatially dependent nodal cross sections. The theory of ANC-H is qualified by benchmarking ANC-H against fine-mesh finite difference code solutions for a variety of benchmark problems. In all cases, the agreement has been excellent. The accuracy of ANC-H for hexagonal geometry cores is as good as ANC for Cartesian geometry cores.