Abstract: Beam-type components with non-uniform cross-sections are widely used in various engineering structures, the dynamic characteristic of which is one of the most important factors in structural design and state evaluation. A non-local numerical model for dynamic characteristic analysis of beams with varying cross-sections is presented by using a peridynamic differential operator (PDDO). The dynamic differential equations and boundary conditions of beams with variable cross-sections are reformulated to a non-local integral form based on PDDO. The natural frequency and vibration mode can be solved by employing the variational analysis and Lagrange multiplier method. A comparison study of beams with constant cross-sections is conducted to validate the accuracy and convergence of this non-local method by comparing the non-local analysis results with analytical solutions in pertinent literatures. The vibrations of two beams with linearly varying and parabolic convex lower surfaces are analyzed, respectively, to verify the applicability and reliability of the method proposed in the free vibration analysis of beams with arbitrarily varying cross-sections. The free vibration of a beam with a hole and parabolic convex lower surface is investigated further to demonstrate the potential of this presented approach in the vibration analysis and damage identification of defective components with non-uniform cross-sections, and which provides a new perspective for the free vibration analysis of defective components with non-uniform cross-sections.