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Geometric error compensation is important in improving the machining accuracy of five-axis machine tools. To improve the efficiency of real-time compensation, this paper proposes a novel compensation method based on a novel representation of the volumetric error. First, 5 error parameters in the workpiece-tool coordinate system are employed to describe the volumetric error, simplifying the actual reverse kinematics from an overdetermined problem to a well-determined problem. Second, the actual inverse kinematics solution, neglecting the position-varying feature of geometric errors, is derived by a simple operation. Finally, the actual inverse kinematics solution considering the position-varying feature of geometric errors is derived based on a linear approximation of geometric errors at the command position nearby. Compared with traditional compensation methods, the proposed method could guarantee higher efficiency since it has a concise analytical expression. Simulation and experiment results are then illustrated to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]