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We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces,with explicit boundary terms.We do this mainly for the Levin-Wen string-net model.The full Hamiltonian in our approach yields a topologically protected,gapped energy spectrum,with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system.We explicitly present the wavefunctions of the ground states and boundary elementary excitations.The creation and hopping operators of boundary quasi-particles are constructed.It is found that given a bulk topological order,the gapped boundary conditions are classified by Frobenius algebras in its input data.Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.