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Hydrodynamic modeling is the basis of the precise control research of underwater manipulators. Viscous hydrodynamics, an important part of the hydrodynamic model, directly affects the accuracy of the dynamic model and the control model of the manipulator. Considering the limited research on viscous hydrodynamics of underwater manipulators and the difficulty in measuring viscous hydrodynamic coefficients, the viscous hydrodynamic model in the form of Taylor expansion is analyzed and established. Through carrying out simulation calculations, curve fitting and regression analysis, positional derivatives, rotational derivatives, and coupling derivatives in the viscous hydrodynamic model, are determined. This model provides a crucial theoretical foundation and reference data for subsequent related research.