<p>One of the more recent methods of solving linear and non-linear equations of physics is the so-called a non-polynomial spline method. The variable coefficient fourth-order parabolic partial differential equations in one space variable arise in the study of the transverse vibrations of a uniform flexible beam. The main objective of this paper is to obtain the approximate solution of super diffusion fourth-order partial differential equations. A fourth-order non-homogeneous parabolic partial differential equation with initial and separated boundary conditions is solved by using a non-polynomial spline method. In the solution of the problem, finite difference discretization in time, and parametric quintic spline along the spatial coordinate have been carried out. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the applied method in this paper is an applicable technique and approximates the exact solution very well.</p>