We have successfully grown large and good-quality single crystals of the La_0.75Sr_0.25Cr_0.90O_3−δ compound using the floating-zone method with laser diodes. We investigated the crystal quality, crystallography, chemical composition, magnetic properties and the oxidation state of Cr in the grown single crystals by employing a combination of techniques, including X-ray Laue and powder diffraction, scanning electron microscopy, magnetization measurements, X-ray photoelectron spectroscopy and light absorption. The La_0.75Sr_0.25Cr_0.90O_3−δ single crystal exhibits a single-phase composition, crystallizing in a trigonal structure with the space group R3̄c at room temperature. The chemical composition was determined as La_0.75Sr_0.25Cr_0.90O_3−δ, indicating a significant chromium deficiency. Upon warming, we observed five distinctive characteristic temperatures, namely T₁=21.50(1) K, T₂=34.98(1) K, T₃=117.94(1) K, T₄=155.01(1) K, and T_N=271.80(1) K, revealing five distinct magnetic anomalies. Our magnetization study allows us to explore the nature of these anomalies. Remarkably, the oxidation state of chromium in the single-crystal La_0.75Sr_0.25Cr_0.90O_3−δ, characterized by a band gap of 1.630(8) eV, is exclusively attributed to Cr^3＋ ions, making a departure from the findings of previous studies on polycrystalline materials.