The crystal structures of two new high-pressure AlPO4 phases are reported. One phase synthesized at 6 GPa and 1523 K is triclinic (P\bar 1) whilst the other phase synthesized at 7 GPa and 1773 K is monoclinic (P2_1/c). 31P MAS (magic-angle spinning) NMR suggests three tetrahedral P sites with equal abundance in both phases. 27Al 3Q MAS NMR spectra provided evidence for two octahedral sites and one five-coordinated Al site in each phase. The crystal structures were solved using an ab initio structure determination technique from synchrotron powder X-ray diffraction data utilizing the local structural information from NMR, and were further refined by the Rietveld method. Both phases contain doubly bent chains made of six edge-shared Al polyhedra (including five-coordinated Al), which are joined by PO4 tetrahedra. The P\bar{1} phase is isostructural with FeVO4 and AlVO4. The two phases differ in the packing manner of the chains. This study has demonstrated that the combined application of ab initio structure determination via X-ray powder diffraction and solid-state NMR spectroscopy is a powerful approach to the rapid solution of complex inorganic crystal structures.