A numerical model for incompressible flows in complex geometries is proposed by using multi-moment VSIAM3 scheme and immersed boundary method.Incompressible N-S equations are discretised by VSIAM3 scheme and complex and moving boundaries are treated with immersed boundary method.Immersed-boundary source terms in momentum equations are effectively represented by an extrapolated velocity field in ghost cells across the interface.Continuity equation is modified to take into account effective fluxes in boundary cells.With multi-moment VSIAM3 scheme uses local high-order reconstruction and collocated grids which are suited well for implementing immersed boundary method with high computational efficiency.The proposed scheme is verified by widely used benchmark test problems.Numerical results are fairly comparable to other existing methods.