  We study the Hubbard model on the honeycomb lattice with nearest-neighbor
hopping ($t>0$) and next-nearest-neighbor one ($t'<0$). When $t'<-t/6$, the
single-particle spectrum is featured by the continuously distributed Van-Hove
saddle points at the band bottom, where the density of states diverges in
power-law. We investigate possible unconventional superconductivity in such
system with Fermi level close to the band bottom by employing both random phase
approximation and determinant quantum Monte-Carlo approaches. Our study reveals
a possible triplet $p+ip$ superconductivity in this system with appropriate
interactions. Our results might provide a possible route to look for triplet
superconductivity with relatively-high transition temperature in a low-filled
graphene and other similar systems.
