A numerical investigation is performed into the characteristics of an electro-osmotic pump consisting of a negatively charged conical nanopore. It is shown that the dependence of the flow rectification effect on the bias direction is the reverse of that of the ion current rectification effect. Moreover, the nozzle mode (i.e., the bias is applied from the base side of the nanopore to the tip side) has a higher flow rate compared to the diffuser mode (i.e., the bias is applied from the tip side of the nanopore to the base side). The results showed that the ion-concentration polarization effect occurred inside the conical nanopore, resulting in surface conduction dominating in the ionic current. The ions inside the nanopore are depleted and enriched under the nozzle mode and the diffuser mode, respectively. As a result, the electro-osmotic pump yields a greater pumping pressure, flow rate, and energy conversion efficiency when operating in the nozzle mode. In addition, we also investigated the flow rate rectification behavior for the conical nanopore. The best flow rate rectification factor in this work is 2.06 for an electrolyte concentration of 10(-3) M.