We are interested in the numerical solution of the large nonsymmetric shifted linear system,(A+αI)x=b,for many different values of the shift α in a wide range.We apply the Saad’s flexible preconditioning technique[14]to the solution of the shifted systems.Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range.Numerical experiments report the effectiveness of our approach on some problems.