Enabling a leading-edge vortex (LEV) is a possible mechanism to significantly increase the lift on wings. This is well known for slender delta wings, for which various analytical models were developed and shown accurate predictions of the lift enhancement. By suitably designing the wing planform, LEVs can also exist on high aspect ratio (AR) wings. This is a three-dimensional effect and in this study, we present a pseudo-three-dimensional flow model for solving the stationary LEV phenomenon over a high AR swept back wing, with sweep increasing towards the wingtip. Our model captures the phenomenon by satisfying conservation of mass and vorticity within the LEV, and using a combination of strip theory and the lifting-line theory. An example of a parabolic swept back wing, confirms that wing geometry can have a major role in holding a LEV steadily over the upper wing surface, resulting in significant lift enhancement of up to 70% in certain cases.