Understanding the electroosmotic flow through a nanochannel is essential to the design of novel nanofluidic devices, ranging from desalination to nanometer water pumps. Nonetheless, the competition between cation and anion in electric fields inevitably leads to a limited pumping of water, and thus weakening their competition could be a new avenue for the fundamental control of water transport. In this work, through a series of molecular dynamics simulations, we find a surprising phenomenon in which under the drive of a traditional longitudinal electric field, an additional lateral electric field can significantly weaken the competitive transport of a cation and anion through a carbon nanotube, which spontaneously leads to a massive increase in electroosmotic water flux. Specifically, with the increase in the lateral electric field, the anion flux exhibits an almost linear reduction, and the cation flux is stable and can even be enhanced. As a result, the net water flux along the cation direction increases significantly. The key to this unexpected phenomenon lies in the size and mobility difference between the cation and anion. The anion is larger and has greater mobility and is thus more susceptible to the lateral electric field, which ultimately leads to the reduction of its flux. For different ion types and CNT lengths, we can observe similar electropumping phenomenon, where the friction force induced by the lateral electric field becomes nontrivial for long CNTs. Our results provide a new route to tune the competitive transport of cations and anions and should be useful for the design of novel electroosmotic pumps.