The atomic and electronic structures of a graphene monolayer on a Ru(0001) surface under compressive strain are investigated by using first-principles calculations. Three models of graphene monolayers with different carbon periodicities due to the lattice mismatch are proposed in the presence and the. absence of the Ru(0001) substrate separately. Considering the strain induced by the lattice mismatch, we optimize the atomic structures and investigate the electronic properties of the graphene. Our calculation results show that the graphene layers tu into periodic corrugations and there exist strong chemical bonds in the interface between the graphene N x N superlattice and the substrate. The strain does not induce significant changes in electronic structure. Furthermore, the results calculated in the local density approximation (LDA) are compared with those obtained in the generalized gradient approximation (GGA), showing that the LDA results are more reasonable than the GGA results when only two substrate layers are used in calculation.