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In this paper, nonlocal symmetries and exact solutions of variablecoefficient Korteweg-de Vries (KdV) equation are studied for the first time.Using pseudo-potential, high order nonlocal symmetries of time-dependentcoefficient KdV equation are obtained. In order to construct new exact analyticsolutions, new variables are introduced, which can transform nonlocalsymmetries into Lie point symmetries. Furthermore, using the Lie pointsymmetries of closed system, we give symmetry reduction and some exact analyticsolutions. For some interesting solutions, such as interaction solutions amongsolitons and other complicated waves are discussed in detail, and thecorresponding images are given to illustrate their dynamic behavior.

High order nonlocal symmetries and exact solutions of variable coefficient KdV equation