We investigated the crystal structure and magnetic structure in cobaltite-platinate double perovskite of La2CoPtO6, employing various techniques of X-ray diffraction, neutron diffraction, and the extended X-ray absorption fine structure analysis. It is shown that the crystal symmetry is maintained as P21/n in the temperature range of <500 °C, whereas the lattice constants and the Co-Co distances undergo a continuous structural evolution toward the high-symmetry phases with increasing temperature. The Co-O bonds were overall longer and had a larger degree of structural and thermal disorders than the Pt-O bonds. As for the magnetism, an antiferromagnetic order is stabilized in the Co2+ sublattice at temperatures below 28 K. It is demonstrated that owing to the substantial distortions (quantified by a distortion parameter Σ > 0.03 Å) of the Co-Co networks, the system is not subject to spin frustration effect. Details in the magnetic structure are determined; at 12 K, the Co magnetic moment was (0.8, 0, 2.7) Bohr magneton, the magnetic propagation vector was (-0.5, 0, 0.5), and the magnetic symmetry was preferably Γ1(Ag).