Flow computations have been performed in vaneless diffuser (diam, 1 m), in low speed backswept centrifugal compressor using finite volume method (FVM),coupled with Standard k-epsilon turbulent model by solving oil commercial package FLUENT assuming steady, incompressible flow condition with design flow-rate in Navier-Stokes equations. Mean velocities and pressure have been computed on eight planes through the diffuser. Flow field at diffuser entry clearly shows impeller jet-wake flow pattern and the blade wakes. Passage wake is located on shroud side of diffuser and mixes Out slowly as flow moves through diffuser. On the other hand, blade wakes distort and mix out rapidly in diffuser. Contours of turbulent kinetic energy are also presented on each of the diffuser stations, from which regions of turbulent mixing are identified. Close agreement was observed between numerical simulation and experimental results.