Ba10Fe3Sb7Se24 was synthesized using a KBr flux at 850 degrees C (Crystal Data: orthorhombic, Cmc2(1), a = 9.3412(2) angstrom, b = 44.6666(10) angstrom, c = 12.5496(3) angstrom, V = 5236.2(2) angstrom(3), and Z = 4). The compound adopts a new three-dimensional framework constructed by the layer to include Fe2Se6 dimers and FeSe4 tetrahedra in the linkage motifs of [Fe2SbSe10] and [FeSb6Se14], respectively. Alternatively, the all Sb-based polyhedra are assembled as a semiconducting, perovskite-like framework lacking an inversion center where these Fe-based magnetic units are trapped within the interstices. The strong antiferromagnetic interaction is revealed by a high Curie constant of -113 K, but the curvature of field-cooled and zero-field-cooled magnetic susceptibilities bifurcating at similar to 19 K is observed. The critical temperature is well verified by a broad peak of chi(M)'' signal showing a rapid increase below 19 K under an alternating current field. The Fe2Se6 dimer featuring distorted edge-sharing tetrahedra to induce the spin-canted antiferromagnetic ordering strongly dominates such magnetic ordering. Finally, a weak hysteresis loop is clearly observed at 2.0 K. This dilute magnetic selenide displays a direct bandgap at similar to 4.54 eV, analyzed by the Tauc equation. Interestingly, the use of second-harmonic-generation temperature dependence shows a turning point at similar to 20 +/- 1 K, which precisely corresponds to the magnetic ordering temperature within the error bar, thereby demonstrating the versatility of the technique for probing magnetic phase transition.