Carrier transport in the hexagonal columnar mesophase of a discogen with a built-in dipole moment in the core—hexaalkoxydibenzo[a,c]phenazine (HDBP-3) was investigated. The temperature and field dependences of bipolar carrier mobilities up to the order of 10−3cm2V−1s−1 in the homeotropically aligned HDBP-3 have been revealed by time-of-flight (TOF) measurement. One-dimensional hopping model was used to discuss the effect of built-in donor–acceptor molecular dipole in the core. The calculation of charge transfer integral also supported the results of mobility measurement. The donor–acceptor molecular dipole in the discogen not only stabilized the mesophase but also contributed to the nondispersive ambipolar nature and substantially enhanced the electron transport in HDBP-3.