Analytical studies of the effect of edge decoration on the energy spectrum of semi-infinite one-dimensional （1D） model and zigzag edged graphene （ZEG） are presented by means of transfer matrix method, in the frame of which the conditions for the existence of edge states are determined. For 1D model, the zero-energy surface state occurs regardless of whether the decorations exist or not, while the non-zero-energy surface states can be induced and manipulated through adjusting the edge decoration. On the other hand, the case for the semi-infinite ZEG model with nearestneighbour interaction is discussed in the analogous way. The non-zero-energy surface states can be induced by the edge decoration and moreover, the ratio between the edge hopping and the bulk hopping amplitudes should be within a certain threshold.
