This work presents an approximate Riemann solver to the transient isothermal drift-flux model. The set of equations constitutes a non-linear hyperbolic system of conservation laws in one space dimension. The elements of the Jacobian matrix A are expressed through exact analytical expressions. It is also proposed a simplified form of A considering the square of the gas to liquid sound velocity ratio much lower than one. This approximation aims to express the eigenvalues through simpler algebraic expressions. A numerical method based on the Gudunov's fluxes is proposed employing an upwind and a high order scheme. The Roe linearization is applied to the simplified form of A. The proposed solver is validated against three benchmark solutions and two experimental pipe flow data. Copyright (c) 2015 John Wiley & Sons, Ltd.809536568Petrobras [0050-0075324.12.2]