The basic idea of this article is to investigate the numerical solutions of Gardner Kawahara equation, a particular case of extended Korteweg-de Vries (KdV) equation, by means of finite element method. For this purpose, a collocation finite element method based on trigonometric quintic B-spline basis functions is presented. The standard finite difference method is used to discretize time derivative and Crank-Nicolson approach is used to obtain more accurate numerical results. Several numerical examples are presented and discussed to exhibit the feasibility and capability of the finite element method and trigonometric B-spline basis functions. More specifically, the error norms $L_{2}$ and $L_{\infty }$ are reported for numerous time and space discretization numbers in tables. Graphical representations of the solutions which describe motion of wave are presented.