Novel calamitic liquid crystals with asymmetrically substituted structure base on the dibenzo[c,h][2,6]naphthyridine (DBN) moiety as an electron-deficient core, 2-(4-decylphenyl)dibenzo[c,h][2,6]-naphthyridine (C10-Ph-DBN), 2-chloro-8-decyl-DBN (Cl-DBN-C10) and 2-decyl-8-phenyl-DBN (Ph-DBN-C10), were synthesized and their carrier transport properties were investigated. The lower ordered smectic phase of SmA emerged in a very wide temperature range of 130 degrees C in all DBN derivatives, which allowed us to study the carrier transport properties in SmA phase in detail for the first time: we purified Cl-DBN-C10 enough to evaluate the carrier transport property in the SmA phase by time-of-flight method. It showed the temperature and electric field dependence of the mobility, indicating the energetic disorder of transport levels. We analyzed it within the framework of the Gaussian disorder model for electrons and obtained a Gaussian width of the density of states to 109meV in the SmA. This is the first experimental result analyzed for the SmA phase in calamitic liquid crystals with nonnegligible dipole moment.