Previous numerical tests have shown that the modified ghost fluid method (MGFM) [T.G. Liu, B.C. Khoo, K.S. Yeo, Ghost fluidmethod for strong shock impacting on material interface, J. Comput. Phys. 190 (2003) 651–681; T.G. Liu, B.C. Khoo, C.W.Wang,The ghost fluid method for compressible gas-water simulation, J. Comput. Phys. 204 (2005) 193-221] is robust and performs muchbetter than the original GFM [R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces inmultimaterial flows (the ghost fluid method), J. Comput. Phys. 152 (1999) 457-492]. In this work, a rigorous analysis is carriedout on the accuracy of the MGFM when applied to the gas-gas Riemann problem. It is shown that at the material interface theMGFM solution approximates the exact solution to at least second-order accuracy in the sense of comparing to the exact solutionof a Riemann problem. On the other hand, the results by the original GFM have generally no-order accuracy if the interface is notin normal motion.