The new compound LiNaCo[PO4]F was synthesized by a solid state reaction route, and its crystal structure was determined by single-crystal X-ray diffraction measurements. The magnetic properties of LiNaCo[PO4]F were characterized by magnetic susceptibility, specific heat, and neutron powder diffraction measurements and also by density functional calculations. LiNaCo[PO4]F crystallizes with orthorhombic symmetry, space group Pnma, with a = 10.9334(6), b = 6.2934(11), c = 11.3556(10) angstrom, and Z = 8. The structure consists of edge-sharing CoO4F2 octahedra forming CoFO3 chains running along the b axis. These chains are interlinked by PO4 tetrahedra forming a three-dimensional framework with the tunnels and the cavities filled by the well-ordered sodium and lithium atoms, respectively. The magnetic susceptibility follows the Curie Weiss behavior above 60 K with theta = -21 K. The specific heat and magnetization measurements show that LiNaCo[PO4]F undergoes a three-dimensional magnetic ordering at T-mag = 10.2(5) K. The neutron powder diffraction measurements at 3 K show that the spins in each CoFO3 chain along the b-direction are ferromagnetically coupled, while these FM chains are antiferromagnetically coupled along the a-direction but have a noncollinear arrangement along the c-direction. The noncollinear spin arrangement implies the presence of spin conflict along the c-direction. The observed magnetic structures are well explained by the spin exchange constants determined from density functional calculations.