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In this paper, we studied a semidiscrete coupled equation, which is integrable in the sense of admitting Lax representations. Proposed first by Vakhnenko in 2006, local conservation laws and one-fold Darboux transformation were presented with different forms, respectively, in O. O. Vakhnenko, J. Phys. Soc. Jpn. ? 84 , 014003 （2015）; O. O. Vakhnenko, J. Math. Phys. ? 56 , 033505 （2015）; O. O. Vakhnenko, J. Math. Phys. ? 56 , 033505 （2015）. On the basis of these results, we principally construct N -fold Darboux transformation by means of researching gauge transformation of its Lax pair, and work out its explicit multisolutions. Given a set of seed solutions and appropriate parameters, we can calculate two-soliton solutions and plot their figures when N = 2 .
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