A new quaternary arsenide Zintl phase, Ba13Si6Sn8As22, has been synthesized from the Sn-flux reactions, and the structure was determined by the single-crystal X-ray diffraction methods. The compound crystallizes in the tetragonal non-centrosymmetric space group I42m (No. 121) with unit cell parameters of a = b = 14.4857(3) Å, c = 13.5506(7) Å, V = 2843.40(17) Å(3). Its polyanion structure can be viewed as composed of [Si4As10] adamantane-like clusters and SiAs4 tetrahedra, which are linked via the [Sn2As4] groups built through two edge-sharing SnAs3 triangular pyramids. Differential thermal analysis and thermogravimetry measurements indicate that Ba13Si6Sn8As22 has good thermal stability, and does not melt or decompose below 1045 K under Ar atmosphere. Density functional calculations were performed on Ba13Si6Sn8As22 and the results suggest a band gap of around 1.0 eV for Ba13Si6Sn8As22, confirmed by the diffuse reflectance spectrum measurement. In addition, the extensively existing lone pairs of electrons on the p-orbitals of As and Sn may also hint interesting nonlinear optical properties considering the noncentrosymmetric structure.