Thehigh-order harmonic generation (HHG) by local field enhancement is investigated using two-centermolecule H2+ with fixed nuclear separation,which is initially prepared in coherent superposition of ground state and first excited state.Using asymmetric-spatial mask functions,multi-trajectory contributions apparently revealed in the harmonic spectra.Based on our analysis,all the trajectories can be controlled by the carier-envelop phase of intense few-cycle laser field.