Abstract In this project we present an iterative process which converges strongly to a common fixed point of a family of Lipschitzian pseudocontractive mappings. The basic concepts of common fixed point of a family of Lipschitzian pseudocontractive mappings has been demonstrated and unify most of the results that have been verified for this important class of nonlinear operators. The algorithm provides a convergence sequence to a common fixed point of a finite family of Lipschitzian pseudocontractive mappings. In addition, it also provides a convergence sequence to a common zero of a finite family of Lipschitzian monotone mappings.