Dynamic tensions of mooring lines may be ignored in the estimation of wave frequency motions of a floating structure, but for slow drift oscillations hydrodynamic forces acting on mooring lines are important, because drag forces acting on mooring lines act as the damping force and have a great effect on the slow drift oscillation. When dynamic tensions of mooring lines are calculated in full consideration of added mass forces and drag forces acting on mooring lines, a numerical calculation such as Lumped Mass Method is usually used. The numerical calculation needs prohibitively long computer time and it is not practical in the early stage of the design of a floating structure. The authors had developed an Approximate Method for calculating the dynamic tension taking the added mass force and drag force into consideration. A remarkable feature of this calculation method is its short computation time, and the accuracy of the approximate method has been confirmed by comparing calculated results with experiments. The original form of the Approximate Method was applicable to the only frequency domain problem and therefore it was impossible to apply the calculation method to the problem in irregular waves. In this paper a Modified Approximate Method extended to the time domain problem is presented. The calculated results of the slow drift oscillation of a floating structure and dynamic tensions of mooring lines obtained by using the extended approximate method are compared with the experimental ones. The calculated results are in good agreements with experimental ones.