New approach is developed in this paper for mode matching of LTI models at different grid points such that a Linear Parameter Varying model can be obtained through interpolation. The approach is based on matching eigenvector associated with each eigenvalue such that state consistency can be guaranteed for local LTI models. The novelty of the developed approach is the ability to handle mode veering phenomena, where two distinct real poles converge into two repeated ones then separate into complex conjugate poles and vise versa. Linear interpolation procedure based on Least-Squares errors is also presented to interpolate local LTI models. The proposed approach is demonstrated through numerical example.