Increase in the Néel temperature (TN) of the 10-nm thick Cr2O3(0001) thin films by the lattice strain was experimentally investigated. TN was determined based on the zero-offset anomalous Hall measurements for the Pt/Cr2O3/Pt epitaxial trilayer. The lattice strain was altered by the Pt buffer layer thickness and was evaluated by the lattice parameters. TN was increased from 241.5 to 260.0 K by varying the Pt buffer layer thickness from 0 to 20 nm. For the film without the Pt buffer layer, the apparent critical exponent near TN increased suggesting the distribution of TN due to the inhomogeneous strain. The TN value was weakly correlated with the axial ratio c/a and the lattice volume of the Cr2O3 layer V; TN increases with decreasing c/a or increasing V. The increase in TN by the reduction in c/a (or by increasing V) implies that the exchange coupling between the nearest neighbor Cr3+ spins has the significant role in the strain effect.