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The Lie group Denavit–Hartenberg method and application in the parallel hexapod robot are researched. The hexapod robot and the ground form opened and closed loop alternately; the complete kinematics equation cannot be derived by Denavit–Hartenberg method with a trigonometric function type. The complete kinematics model of the hexapod robot is constructed with the improved Denavit–Hartenberg method. The numerical solving strategy is schemed. The simulation results provide the positive and athwart kinematics response relation during the lift and forward patterns in space. The research shows that the complete kinematics model can be constructed by the Lie group Denavit–Hartenberg method; the numerical calculation method can solve the pose–attitude response correctly.