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A high order boundary element method was developed for the complex velocity potential problem.The method ensures not only the continuity of the potential at the nodes of each element but also the velocity.It can be applied to a variety of velocity potential problems.The present paper,however,focused on its application to the problem of water entry of a wedge with varying speed.The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem,because when the time stepping method is used,the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial.Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dt2,where D and a are constants,which is found to lead to a self similar flow field when the effect due to gravity is ignored.