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In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t ＞ 0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point ū ∈(R).