The antiferromagnetic insulator La 1.5 Ca 0.5 CoO 4 has been investigated by Co L 2,3 -edge and O K-edge X-ray absorption spectroscopy (XAS) measurements and Co L 2,3 -edge resonant soft X-ray magnetic scattering (RXMS) measurement to determine the Co electronic structures associated with magnetic ordering. Co L 2,3 -edge linear-dichroic XAS shows that Co 2+ takes a high-spin (HS) state and Co 3+ takes a low-spin (LS) state. Using Co L 2,3 -edge RXMS, we directly determined that an antiferromagnetic order is formed with a HS state of Co 2+ ions. Moreover, the spin and orbital angular momenta of the Co 2+ HS state are quantitatively estimated to be 1.1 « 0.1 and 1.0 « 0.1, respectively, and to align parallel in the ab plane by utilizing the cluster model calculation. The large orbital angular momentum of the Co 2+ HS state originates from the small D 4h -symmetry crystal field splitting of t 2g levels, which is comparable with the spin-orbit coupling constant of the Co 3d orbital.