A robust implicit method for turbulent two-phase flows at all-speeds on unstructured grids has been proposed here. Unlike conventional compressible two-phase methods, the presented method does not employ exact Riemann solvers for robustness in vicinity of two-phase interfaces, thus making it very efficient. Instead, appropriate improvements are made in the AUSM+-up flux to impart required robustness near material interfaces. These improvements consist of an appropriate scaling for the velocity diffusion/coupling terms and a modification in the mass-flux calculations based on the relative velocity. This work is an extension of previous work on a finite-volume method for viscous two-phase flows, where an implicit method was proposed to solve flows at all-speeds. All-speed capability is crucial since most of the traditional multiphase applications involve low speed flows (Mα≈ 10− 4) which cannot be solved using the standard density-based algorithms. The presented method uses a transformation to primitive variables to deal with such low Mach number flows. This, in addition to the appropriate scaling and coupling terms in the inviscid fluxes result in a truly all-speed capable two-phase flow method, which was shown to perform well at a range of Mach numbers. In the present work, the Spalart-Allmaras turbulence closure is used to model the Reynolds stresses of the continuous phase in the Favre-averaged two-fluid system. The turbulence in the dispersed phase is not separately modeled, but connected to the continuous phase turbulence through a response coefficient. The resulting method is shown to accurately resolve the averaged flow quantities, in comparison to boilEulerFOAM, a pressure-based multiphase solver.