Based on log-conformation method developed recently,a log-conformation-based fractional step algorithm with stabilization mechanism is proposed by virtue of the finite increment calculus(FIC)process.The algorithm remarkably reduces computational cost within each iteration step compared with existed coupled solution schemes.Meanwhile it bypasses finite difference approximation for gradient of conformation tensor.As FIC process is introduced as pressure stabilization mechanism,restrictions on u-p interpolations imposed by LBB compatibility conditions are circumvented and equal-lower-order interpdlations for u-p are allowed to apply.Numerical simulations for cylinder flow show excellent stabilization and accuracy of the proposed algorithm.