Anthoinite, AlWO3(OH)3, from the Mt. Misobo Mine, Democratic Republic of the Congo, has triclinic symmetry with cell parameters a = 8.196(1) Å, b = 9.187(1) Å, c = 11.316(1) Å, α = 92.82(1)°, β = 94.08(1)°, γ = 90.23(1)°, space group I1̅, Z = 8. The structure was solved by applying ab initio structure solution methods (Reverse Monte Carlo/Simulated Annealing) to both X-ray and neutron powder diffraction data and was refined using the Rietveld method. The structure is built up of two types of M4(O,OH)16 planar tetrameric clusters of edge-sharing octahedra, one containing predominantly Al and the other predominantly W. The Al-rich and W-rich clusters interconnect via corner sharing to form stepped layers parallel to (001). The layers are held together by strong hydrogen bonding. The structure can be described as a rocksalt derivative structure, with the close-packed anion layers parallel to (012), and with Al and W atoms ordered into one third of the octahedral sites within the cubic close-packed anion lattice. The structure is complicated by partial disorder between Al and W in the tetrameric clusters and associated disorder in the H atom sites. Infrared and 27Al MAS NMR results are also presented for anthoinite.