We extended the pruned-enriched Rosenbluth method, which was proposed by Grassberger for simulating a single self-avoiding walk （called GR method for the sake of convenience）, to simulate multi-avoiding walks. For simplicity this method is called extended GR （E-GR） method and used to investigate the screening behavior of linear polymer solutions. The simulations show that the screening is a cooperative behavior of monomers on other chains, i.e. it is not only dependent on the concentration of solutions but also on the length of other chains. The simulated screening behavior agrees with the experiments and the prediction of the self-consistent field theory. These results also show the validity and potential applications of E-GR to study other physical properties of linear polymer solutions.