The effects of environmental fluctuations on a model system of biomolecular self-replication are investigated by considering the relevant rate parameters as being subjected to white-noise fluctuations. The steady state properties of the model are studied in detail by analyzing the probability function and the moment equations. New phase diagram are devised to describe stochastically the nonequilibrium phase transition. The effects of various noises on the steady state replications can thus be compared in a direct and apparent way.