A numerical-analytical modeling technique was presented for predicting instantaneous energy absorption with axial tidal turbines in unsteady water flow. The goal of present paper is introducing a fast and stable integral solution approach with unique solution. This technique employs steady-state CFD data to approximate transient performance of axial tidal turbine in unsteady external flows. This solution technique was designed for modeling axial tidal turbine with convergent-divergent duct in water flow with unsteady boundary conditions. The governing equations for fluid flow were derived in the form of integral equations. The equation of one-degree of freedom motion for rotor was solved with fourth-order Runge-Kutta method and variation of parameters approach. CFD data for rotor and duct of axial tidal turbine were inserted as boundary values in integral equations of fluid flow. Two transient analytical equations were employed for approximating rotor torque and back pressure coefficient of tidal turbine. The results of integral solution approach were compared with transient CFD data in ANSYS-Fluent software. Many numerical simulations were performed to determine duct dimensions for maximum power enhancement in an axial tidal turbine.