In this paper, a non-centrosymmetric compound of Rb₂Ca₂(SO₄)₃ has been synthesized by a high temperature solid-state reaction and high temperature melting method. Single-crystal X-ray diffraction analysis shows that Rb₂Ca₂(SO₄)₃ crystallizes in the cubic space group of P2₁3, and its cell parameters are a = b = c = 10.5569(6) Å, Z = 4 and V = 1176.55(12) ų, respectively. In the crystal structure, SO₄ tetrahedra and CaO₆ octahedra are connected with each other by a corner-sharing mode to construct the three-dimensional framework of Rb₂Ca₂(SO₄)₃. Optical measurements show that the title compound has a short ultraviolet absorption edge and a moderate second-harmonic generation response. The optical origin is illustrated by the electron band structure calculation. In addition, thermal stability is also studied by virtue of differential thermal/thermogravimetric analysis and powder XRD technique.