In this study, we theoretically investigate the ballistic thermoelectric performance of a new two-dimensional material, nitrogenated holey graphene (NHG), using nonequilibrium Green's function method. The calculations show that compared to graphene, such novel single atomic layer structure exhibits better thermoelectric performance. At room temperature, the stable hole (electron) thermoelectric figure of merit (ZT) could approach 0.75 (0.2) and 0.6 (0.2) for zigzag-edged (Z-NHGNRs) and armchair-edged NHGNRs (A-NHGNRs), respectively. To achieve better thermoelectric performance, the effect of geometric engineering (chevron-type nanoribbons and rhomboid quantum dot) on the electronic and phononic transport properties of Z-NHGNRs is further discussed. The results indicate that structure modulation is indeed a viable approach to enhance the thermoelectric properties (the figure of merit could exceed 1.5 and 1.3 for the chevron-type and rhomboid quantum dot system, respectively). On analyzing the transport properties, such improvement on the figure of merit is mainly attributed to the increased Seebeck coefficient and reduced thermal conductance (including both electronic and phononic contributions). Our findings presented in this paper qualify NHG as a promising thermoelectric material and provide theoretical guidance for fabricating the outstanding thermoelectric devices.