The layered cobaltite Sr2CaYCo4O10.5 with formal average cobalt oxidation state close to 3+ has been studied as functions of both temperature and pressure up to 4GPa by neutron powder diffraction (NPD). The crystal structure is shown to have tetragonal symmetry (space group I4/mmm; 2a(p) x 2a(p) x 4a(p) superstructure), and the magnetic structure at ambient pressure is found to be G-type antiferromagnetic with T-N close to 310 K. The magnetic moments within the CoO6 octahedral layers and anion-deficient CoO4.5 layers are 1.2 mu(B) and 2.8 mu(B), respectively. At 25K, and applied pressure of 3.5 GPa is sufficient to completely suppress a long-range magnetic order. This result is interpreted in terms of a pressure-induced high-to-low spin state crossover of the Co3+ ions.