The constraints on the physical limit should be considered in a kinematic redundancy resolution problem of a robot. This paper proposes a new optimization scheme to resolve kinematic redundancy of the robot while considering physical constraints. In the proposed scheme, quadratic inequality constraints are used in place of linear inequality constraints, thus a quadratically constrained optimization technique is applied to resolve the redundancy. It is shown that the use of quadratic inequality constraints considerably reduces the number of constraints. Therefore, the proposed method reduces the problem size considerably and makes the problem simple resulting in computational efficiency. A numerical example of a 4-link planar redundant robot is included to demonstrate the efficiency of the proposed optimization technique. In this example, simulation results using the proposed method and another well-known method are compared and discussed.