Graphene is a promising material for thermoelectric application due to its large surface-to-volume ratio, high electrical conductivity, and high mechanical strength. In this paper, the thermoelectric properties of a series of narrow armchair graphene nanoribbons (GNR) in semiconducting family GNR(3p+1,0) are evaluated by using the semi-classical Boltzmann theory. It is found that the narrow GNR(7,0) exhibits small thermal conductivity and large TEP of 1170μV / K at small chemical potential μ = 0.1 eV . However, the small electrical conductivity of narrow GNR(7,0) suppresses the thermoelectric figure-of-merit ZT, such that better thermoelectric performance of ZT > 0.01 is achieved only for large chemical potentials, μ > 0.5eV . Our result shows that tuning the chemical potential with respect to ribbon chirality and orientation can enhance the thermoelectric performance of GNRs, however, further increase in thermoelectric power requires phonon engineering to reduce the thermal conductivity of graphene without significant reduction in its thermoelectric power and electrical conductivity.