La₂CoO_4+δ is a strongly correlated oxide with exciting physical and electronic properties originating from the subtle interplay of the lattice, orbital, charge, and spin degrees of freedom. In particular, oxygen-rich La₂CoO_4.25 is a key compound for studying oxygen and electronic ordering phenomena and their correlation. Single-crystal growth of these phases has been plagued by difficulties related to their incongruent melting. In this work, we report on the growth and characterization of high-quality, centimeter-sized La₂CoO_4.25 single crystals, suitable for neutron scattering experiments. La₂CoO_4+δ single crystals were grown by the traveling solvent floating zone without the addition of a solvent but continuously stabilizing the growth conditions. Postsynthesis annealing at 500 °C in oxygen flux yielded phase-pure La₂CoO_4.25, which was further characterized by single-crystal neutron and X-ray diffraction, as well as by scanning electron microscopy with energy-dispersive X-ray spectroscopy, revealing its quality in terms of composition, homogeneity, and crystalline quality. For La₂CoO_4.25, a complex structure with a two-dimensional modulation vector related to oxygen ordering was revealed by single-crystal X-ray and neutron powder diffraction studies. In addition, magnetic measurements coupled with preliminary single-crystal elastic neutron scattering experiments exhibited antiferromagnetic ordering with a Néel temperature (T_N) of 36 K with a complex magnetic structure involving the doubling of all orthorhombic axes.