An electrokinetic model for a wavy capillary has been developed. Poisson-Nernst-Planck and Navier-Stokes equations constitute the model that governs fluid and ionic fluxes and electric potential distribution inside the capillary. In the present paper, a finite wavy cylindrical capillary with a large reservoir at both capillary ends is analyzed using finite element method. The model is used primarily to examine the influence of capillary surface waviness on the electrokinetic transport behaviours. Different frequencies and amplitudes of the wavy surface are considered to investigate the influence of surface waviness on electrokinetic transport. Fluctuations in potential and ionic concentration distribution increase with the increase in either amplitude or frequency of the capillary surface waviness. However, for higher frequencies the fluctuation diminishes for all surface waviness amplitudes. It is observed that for any irregularity in the capillary surface results in higher salt rejection. Salt rejection is found to be dependent on capillary axial length as well as flow velocity. A critical Peclet number, beyond which salt rejection attains a constant steady value, dictates maximum salt rejection.