A quantum corrected Poisson-Nernst-Planck (QCPNP) model is proposed for simulating ionic currents through biological ion channels by taking into account both classical and quantum mechanical effects. A generalized Gummel algorithm is also presented for solving the model system. Compared with the experimental results of X-ray crystallography, it is shown that the quantum PNP model is more accurate than the classical model in predicting the average number of ions in the channel pore. Moreover, the electrostatic potential has been found to reach as high as 19% difference between two models around the charged vestibule which has been shown to play a significant role in the permeation of ions through ion-selective ligand-gated or voltage-activated channels. These results indicate that the QCPNP model may be considered as a more refined continuum model that can be incorporated into a multi-scale electrophysiology modeling.