High-order-harmonic generation (HHG) from small linear molecules driven by a circularly polarized laser pulse (CPLP) is investigated. It is found that the obtained high-order harmonics are more pronounced than those from reference atoms with equal ionization potential driven by the same CPLP. By analyzing the dependence of the cutoff position on laser parameters and calculating the recollision trajectories, it is shown that this molecular HHG originates from the recollision mechanism, instead of the bound-bound transition mechanism found to be responsible for molecular HHG by CPLP in earlier works. A semiclassical model is used to analyze the HHG process and discuss the origin of the higher efficiency of molecular HHG. It is found that the higher HHG efficiency for molecules is mainly contributed in the recombination step and at least partly due to the higher recollision probability of continuum electrons.