This paper presents a randomized manipulation planner for a multi-fingered hand by switching contact modes. Manipulation planning for such a system should consider changing kinematics and dynamics of the system according to the contact modes. We derive the conditions that would be satisfied in manipulation planning, based on the kinematical properties of a manipulation system. The conditions allow the planner to assign more contact modes than those corresponding to the relative motion of contact points restricted by constraint forces. Consequently, this enables dextrous manipulation. In addition, the conditions give the restrictions of feasible contact modes and the number of contact points. Inspired by randomized motion planning techniques, we propose a new algorithm for manipulation planning in order to explore object configuration space, SE(3), rapidly and uniformly. The basis for this approach is for the construction of exploring random trees. Simulation examples for 3-D manipulation by switching contact modes are presented to verify the planner's effectiveness.