We investigate nonlocal advantage of quantum coherence(NAQC)in a correlated dephasing channel modeled by the multimode bosonic reservoir.We obtain analytically the dephasing and memory factors of this channel for the reservoir having a Lorentzian spectral density,and analyze how they affect the NAQC defined by the l1 norm and relative entropy.It is shown that the memory effects of this channel on NAQC are state-dependent,and they suppress noticeably the rapid decay of NAQC for the family of input Bell-like states with one excitation.For the given transmission time of each qubit,we also obtain the regions of the dephasing and memory factors during which there is NAQC in the output states.