The normal quaternion method of inverse kinematics of serial mechanisms has the limitation of lacking equations and is difficult to solve. In order to solve these problems and put forward a new method of inverse kinematics of serial mechanisms, a D-H quaternion method for inverse kinematics of serial mechanisms is proposed. The general equation of quaternion transformation including D-H parameters was given first. Two equations of position and posture were obtained by separating the general equation of quaternion transformation. By these two equations, an equation system with seven equations was constructed, which met the number requirement of the equations for inverse kinematics of serial mechanisms with more than four degrees of freedom. In order to lower the difficulty in solving equations, the degree of posture equation was reduced to half by taking half of the trigonometric function in the original posture equation to construct a new posture equation. By using the proposed D-H quaternion method, the inverse kinematics of PUMA robot was analyzed, and eight groups of inverse solutions were obtained. Three dimensional models of PUMA robot were established based on the eight groups of inverse solutions. Measured results of end positions and postures in the three dimensional models are consistent with the given values. The example of PUMA robot shows the correctness and validity of the proposed D-H quaternion method.