A time accurate and stable finite-difference method for gas-liquid two-phase flows was presented and applied to a two-phase shock tube problem. In this method, the artificial dissipation terms in the upwinding process of advection terms were constructed by using the preconditioning matrix to enhance the stability and accurate treatment of gas-liquid two-phase flows with both compressible and incompressible characteristics at arbitrary void fractions. A homogeneous equilibrium gas-liquid two-phase flow model and a stable 4-stage Runge-Kutta method as well as Roe-type flux splitting method with the 3rd order MUSCL TVD scheme were employed. As a numerical example, several two-phase shock tube problems with arbitrary void fractions and Mach numbers were computed, and the applicability and stability of the proposed method to the unsteady problem were checked. From the results, it showed a good prediction and simulation for the unsteady shock tube flow including the propagation of both compression and expansion waves. The effect of applying the preconditioner to the upwinding was confirmed.