A new seamless multiscale simulation was developed for coupling the continuum model with its molecular dynamics. Kriging-based Finite Element Method (K-FEM) is employed to model the continuum base of the entire domain, while the molecular dynamics (MD) is confined in a localized domain of interest. In the coupling zone, where the MD domain overlaps the continuum model, the overall Hamiltonian is postulated by contributions from the continuum and the molecular overlays, based on a quartic spline scaling parameter. The displacement compatibility in this coupling zone is then enforced by the Lagrange multiplier technique. A multiple-time-step velocity Verlet algorithm is adopted for its time integration. The validation of the present method is reported through numerical tests of one dimensional atomic lattice. The results reveal that at the continuum/MD interface, the commonly reported spurious waves in the literature are effectively eliminated in this study. In addition, the smoothness of the transition from MD to the continuum can be significantly improved by either increasing the size of the coupling zone or expanding the nodal domain of influence associated with K-FEM.