We discuss the effect of a strong magnetic field on neutron ^3P_2 superfluidity. Based on the attraction in the ^3P_2 pair of two neutrons, we derive the Ginzburg-Landau equation in the path-integral formalism by adopting the bosonization technique and leave the next-to-leading order in the expansion of the magnetic field B. We determine the (T,B) phase diagram with temperature T, comprising three phases: the uniaxial nematic (UN) phase for B=0, D_2-biaxial nematic (BN) and D_4-BN phases in

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... te B and strong B such as magnetars, respectively, where D_2 and D_4 are dihedral groups. We find that, compared with the leading order in the magnetic field known before, the region of the D_2-BN phase in the (T,B) plane is extended by the effect of the next-to-leading-order terms of the magnetic field. We also present the thermodynamic properties, such as heat capacities and spin susceptibility, and find that the spin susceptibility exhibits anisotropies in the UN, D_2-BN, and D_4-BN phases. This information will be useful to understand the internal structures of magnetars.