The possibility to improve thermoelectric performance of carbon-based quantum devices is of fundamental and importance in the fields of energy conservation, environmental protection, and green energy. Here we propose an effective avenue to enhance the thermoelectric figure of merits (TE-FOMs) of an all-carbon quantum device with the help of first-principles methods, and the device is constructed by a zigzag-edged trigonal graphene (ZTG) connected with zigzag-edged graphene nanoribbons (ZGNR) electrodes through the carbon atomic chains (CACs). Using a gate field, the spin-up transmission peak can be tuned from the position below the Fermi level to that above the Fermi level. However, the position of the spin-down transmission peak above the Fermi level is insensitive to the gate field. Therefore, the device can be converted from the p type to n type for the spin-up component by a gate field, while for the spin-down component the device remains n type. Meanwhile, we also find that the charge (spin) TE-FOMs at the Fermi level can be increased to about eight (three) times as compared with the case in the absence of the gate field. These TE-FOMs can also be significantly improved by tuning the incident electron energy and temperature.