In this paper, by using the asynchronous iteration model presented by Bertsekas [1], a sufficient condition for monotone convergence of asynchronous iterative methods for computing fixed points on a distributed computer is given and the convergence rate shows the asynchronous parallel iterative (method is superior to that of its synchronous counterpart but its communication complexity, however, can be worse. Moreover, by producing a sequence of random vectors, we present a method to simulate an asynchronous parallel environment which can possess arbitrary communication delays like a real distributed computer.