Summary: This paper deals with a robust nonsmooth vector optimization problem related to nonsmooth vector function with the uncertainty in cone-constraint set. We employ robust optimization technique (also called the worst-case approach) for finding (weak) \(e\)-quasi efficient solutions of the robust vector optimization problem. As a consequence, we establish both necessary and sufficient optimality conditions for a feasible solution to be (weak) \(e\)-quasi efficient solutions (i.e., (weak) approximate-quasi efficient solutions) of the considered robust vector optimization problem. Finally, a Wolfe type dual problem in approximate form is formulated, strong and converse robust duality theorems are proposed.