Composite borate-phosphate compounds have always attracted much attention for their structure diversity and interesting properties. In this work, a new borate-phosphate CsNa₂Lu₂(BO₃)(PO₄)₂ (CNLBP) was found for the first time and its structure was characterized by single-crystal X-ray diffraction method. It crystallizes in orthorhombic system, space group Cmcm with a = 6.8750(5), b = 14.6919(1), c = 10.5581(7) Å, V = 1066.44(1) ų, Z = 4, M_r = 777.58, D_c = 4.843 g/cm³, F(000) = 1368, μ(MoKα) = 22.20 mm^-1, R(F² > 2σ(F²)) = 0.0173 and wR(F²) = 0.0367. The structure of CNLBP features a chain framework of [Lu₂(BO₃)(PO₄)₂]_∞ that delimits 1D tunnels filled by Na⁺ and Cs⁺ ions. Phosphors CNLBP:xTb (x = 0, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0) were prepared, and it can emit bright green light under near-UV excitation due to the ⁵D₄→⁷F_j (j = 6, 5, 4, 3) transition of Tb³⁺. Due to the large separation of Lu³⁺ ions in CNLBP structure lattice, the optimal concentration of Tb³⁺ is 80%, and concentration quenching occurs only for the full Tb³⁺ concentration.