The　penalty　and　characteristic-based　operator　splitting　with　multistep　scheme　(penalty-MCBOS)　has　been　developed　for　the　unsteady　incompressible　Navier-Stokes　N-S　equations.　At　each　time　step,　the　N-S　equations　are　split　into　the　diffusive　part,　the　convective　part　by　adopting　the　operator　splitting　method　and　the　pressure　part　by　applying　the　penalty　method　with　low　penalty　parameters.　For　the　diffusive　part,　the　temporal　discretisation　is　based　on　backward　difference　method　and　is　solved　by　preconditioned　conjugate　gradient　(PCG)　method.　For　the　convective　part,　the　temporal　discretisation　is　performed　by　characteristic-Galerkin　method.　It　is　solved　explicitly　and　the　multistep　technique　is　used.　The　pressure　can　be　calculated　from　the　pressure　part　without　necessitating　the　solution　of　the　pressure　Poisson　equation.　The　plane　Poisseuille　flow,　the　lid-driven　cavity　flow,　the　lid-driven　triangular　cavity　flow　and　the　backward-facing　step　flow　are　investigated　to　validate　the　present　model.　It　is　shown　that　the　numerical　results　are　in　good　agreement　with　the　previously　published　data,　and　the　present　model　has　high　efficiency.　For　the　backward-facing　step　problem　at　Re　=　3,000,　the　flow　becomes　periodical　in　time　and　dynamic　evolution　process　of　vortex　can　be　simulated.　Copyright　©　2020　Inderscience　Enterprises　Ltd.