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It has been demonstrated that the zigzag honeycomb nanoribbons exhibit an intriguing edge magnetism.Here the effect of the anisotropy on the edge magnetism in zigzag honeycomb nanoribbons is investigated using two kinds of large-scale quantum Monte Carlo simulations.The anisotropy in zigzag honeycomb nanoribbons is characterized by the ratios of nearest-neighbor hopping integrals t1 in one direction and t2 in another direction.Considering the electron-electron correlation,it is shown that the edge ferromagnetism could be enhanced greatly as t2/|t1| increases from 1 to 3,which not only presents an avenue for the control of this magnetism but is also useful for exnloring further novel magnetism in new nano-scale materials.