A level set formulation of Eulerian interface capturing methods is applied to analyze an interface motion in incompressible gas-liquid two-phase flow. The Navier-Stokes equations in primitive variable formulations are solved on a staggered grid by the method of lines. The advection terms are discretized by QUICK method and the other terms by central finite difference method except for the body force, and a second-order Adams-Bashforth method is used as the time integration scheme. The Poisson equation is solved by means of the Successive Over Relaxation (SOR) approach. The model of Continuum Surface Force (CSF), which interprets surface tension as a continuous effects across an interface rather than as a boundary condition on the interface, is employed to treat the surface tension at the interface. Numerical results are obtained for an oscillation of droplet driven by surface tension at high Reynolds number (1000), head-on collision of two water droplets with large density ratio (1000/1), falling of a water droplet with large density ratio (1000/1), and dam-breaking in the air. It is comfirmed that the present approach is efficient as well as robust and is suitable for numerical solutions to incompressible gas-liquid two-phase flow.