Methods using the Jacobian matrix are quite effective for manipulator inverse kinematic solution except in regions near singular points. Many approaches have been developed to handle the singularity problem. In this paper, an algorithm using damped pseudoinverse with variable damped weight is introduced for inverse kinematic solution. An upper bound of condition number of the Jacobian matrix is established, according to the value of this upper bound, a method to adaptively adjust the damped weight is proposed. The introduced algorithm is stable in regions near singular points and can achieve accurate solution.