An incomplete Cholesky (IC) factorization with multi-parameters is presented. The marked virtue of the proposed IC factorization algorithm is to dynamically control the number of nonzero elements in each column of the IC factorization preconditioner L with the help of these involved parameters. Parameter setting strategies are also given. Numerical results show that the total computing time for both computation of the preconditioner L and iterative solution is evidently reduced for almost all test matrices. In general, these parameters can obviously enhance the effectiveness and performance of the IC factorization. Copyright © 2011 John Wiley & Sons, Ltd.