In this paper, we introduce a new approximating method for
finding the common element of the set of fixed points of nonexpansive
mappings and the set of solution of system variational inequalities for
finite family of inverse strongly monotone mappings and strictly pseudocontractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under
some parameter controling conditions. Our results improve and extend
the results announced by many others.