The recent report of a p-type graphene(Gr)/carbon-nanotube(CNT) barristor facilitates the application of graphene barristors in the fabrication of complementary logic devices. Here, a complementary inverter is presented that combines a p-type Gr/CNT barristor with a n-type Gr/MoS2 barristor, and its characteristics are reported. A sub-nW (~0.2 nW) low-power inverter is demonstrated with a moderate gain of 2.5 at an equivalent oxide thickness (EOT) of ~15 nm. Compared to inverters based on field-effect transistors, the sub-nW power consumption was achieved at a much larger EOT, which was attributed to the excellent switching characteristics of Gr barristors.