This paper proposes an ALE(Arbitrary Lagrangian-Eulerian) finite element method for gas-liquid two-phase flow, based on an incompressible two-fluid model, so as to analyze the two-phase flow including moving boundaries. The conservation equations for the two-fluid model are derived with the use of the ALE method. The solution algorithm is parallel to a fractional step method, and the Galerkin method is employed for the formulation. Quadrilateral element with four nodes is used for the discretization of the calculating domain. The present method is also applied to the calculation of the flow around a cylinder, which is forced to oscillate in air-water two-phase mixture, to demonstrate the validity of the method. The drag coefficients of the cylinder exhibit periodical change in accordance with the variation of the flow around the cylinder. The time variations of the flow field and drag coefficients are discussed in relation to the oscillation of the cylinder.