The inverse kinematics of a general 6R serial robots has much difficulty to be solved.The method using traditional D-H need amount of computations and exists singular solution. Inverse kinematics of puma robot decomposes into position solution and pose solution. Firstly we use D-H method to solve θ₁, θ₂, θ₃, then use the unit quaternion to solve θ₄, θ₅, θ₆. At last we verify the new method in the robot of puma and new method can solve the inverse kinematics correctly. Compared with D-H method and double quaternion method, the new method has much increase about 15% in speed than D-H method.