The dynamical mean-field theory is employed to study the orbital-selective Mott transition (OSMT) of the two-orbital Hubbard model with nearest neighbor hopping and next-nearest neighbor (NNN) hopping. The NNN hopping breaks the particle-hole symmetry at half filling and gives rise to an asymmetric density of states (DOS). Our calculations show that the broken symmetry of DOS benefits the OSMT, where the region of the orbital-selective Mott phase significantly extends with the increasing NNN hopping integral. We also find that Hunds rule coupling promotes OSMT by blocking the orbital fluctuations, but the influence of NNN hopping is more remarkable.