A robust and efficient finite volume method with interface sharpening technique has been developed to solve the six-equation multi-fluid single-pressure model for compressible two-phase flows. The numerical method is implemented in a three-dimensional vertex-centered code. A least-squares reconstruction with Kuzmin's vertex-based (VB) limiter is implemented for the volume fraction and a set of primitive variables in the presented finite volume framework. In regions where two different fluid components are present within a cell, a sharpening technique based on THINC (Tangent of Hyperbola for Interface Capturing) is adopted to provide a sharp resolution for the transitioning interface. These reconstructed values are then used as the initial data for Riemann problems. The enhanced AUSM+ -up scheme is applied to both liquid and gas flows. The multi-stage Runge-Kutta method is used for time marching. A number of benchmark test cases are presented to assess the performance of the present method. These include: an air-water interface moving at a constant velocity, Ransom's faucet problem, air-water/water-air shock tube problems with high pressure ratios, a shock in air impacting a water column case, an underwater explosion case and an air bubble blast case. In all of these cases, the shock and rarefaction waves are captured accurately, especially with the THINC interface sharpening technique. • The single pressure six-equation model is implemented in a three-dimensional vertex-centered code. • The Tangent of Hyperbola interface sharpening technique is implemented. • A number of test cases are presented to show the accuracy of the developed numerical method. • The numerical results in this paper are in good comparison with the literature.