We present a new potential energy surface (PES) for the ground state (1(2)A(')) of the chemical reaction Ne+H(2) (+) from a set of accurate ab initio data, which were computed using highly correlated complete active space self-consistent field and multireference configuration interaction wave functions with a basis set of aug-cc-pV5Z. The quantum reactive scattering dynamics calculation was carried out over the collision energy (E(col)) range of 0.5-1.5 eV based on the new PES. In this work we have taken the Coriolis coupling (CC) effect into account. The importance of including the CC quantum scattering calculation has been revealed by the comparison between the CC and the centrifugal sudden approximation calculation. The magnitude and profile of the CC total cross sections for v=0 and j=1 over the collision energy range of 0.5-1.5 eV are found to be in good agreement with the available experimental measurements obtained recently by Zhang et al. [J. Chem. Phys. 119, 10175 (2003)] after taking into account the experimental uncertainties.