The differential equations of out-of-plane displacements of curved beams with variable curvature have variable coefficients. Selection of the solution method is based on the curvature function of the curved beam. In this study, Differential Quadrature Method (DQM) and Finite Element Method (FEM) are used to find the out-of-plane displacements of curved beams with variable radius of curvature. Since the parabola is very famous and known curve, it is selected as the form of curved beam. To test and validate the computer codes developed based on DQM in Matlab and based on FEM by APDL (ANSYS Parametric Design Language) in ANSYS, some typical examples are considered. As first step, convergence studies are performed to determine the number of sampling points in DQM and number of elements in FEM. After having information about aforementioned modeling parameters, comparisons between DQM and FEM results are given. The effects of variable curvature parameter of the curved beam on out-of-plane displacements are obtained. The practical application of the present model is discussed.