In this paper, one considers the vector saddle point problem with respect to a cone which depends on two parameters. Necessary and sufficient conditions for a point to be a solution of the parameterized cone saddle point problem are given. Then the parameterized cone saddle point problem is related to the parameterized cone vector variational inequality problem. One shows that, under some hypotheses, the problems of parameterized cone vector saddle point and of parameterized cone vector variational inequality have the same solution set. Also, an existence result for a parameterized cone vector saddle point problem to have a solution is given.