Motivated by the recent observations of various exotic quantum states in the equilateral triangular-lattice phosphates Na₂BaCo(PO₄)₂ with J_eff = 1/2 and Na₂BaNi(PO₄)₂ with S = 1, the magnetic properties of spin-5/2 antiferromagnet Na₂BaMn(PO₄)₂, their classical counterpart, are comprehensively investigated experimentally. DC magnetization and specific heat measurements on polycrystalline samples indicate two successive magnetic transitions at T_N1 ≈ 1.13 K and T_N2 ≈ 1.28 K, respectively. Zero-field neutron powder diffraction measurement at 67 mK reveals a Y-like spin configuration as its ground-state magnetic structure, with both the ab plane and c-axis components of the Mn²⁺ moments long-range ordered. The incommensurate magnetic propagation vector k shows a dramatic change for the intermediate phase between T_N1 and T_N2, in which the spin state is speculated to change into a collinear structure with only the c-axis moments ordered, as stabilized by thermal fluctuations. The successive magnetic transitions observed in Na₂BaMn(PO₄)₂ are in line with the expectation for a triangle-lattice antiferromagnet with an easy-axis magnetic anisotropy.