Based on the Eigen model with a single peak fitness landscape， the fitness values of all sequence types are assumed to be random with Gaussian distribution. By ensemble average method， the concentration distribution and error threshold of quasispecies on single peak Gaussian distributed fitness landscapes were evaluated. It is shown that the concentration distribution and error threshold change little in comparing with deterministic case for small fluctuations， which implies that the error threshold is stable against small perturbation. However， as the fluctuation increases， the situation is quite different. The transition from quasispecies to error catastrophe is no longer sharp. The error threshold becomes a narrow band which broadens and shifts toward large values of error rate with increasing fluctuation.