We investigate a Volterra ecosystem driven by correlated noises. The fluctuation in the death rate of the predator induces an increase of population density of the predators. The fluctuation in the growth rate of the prey, however,leads the predators to decay. It is reported that the predators undergo sensitivity to a random environment,whereas the preys exhibit a surprising endurance to the same stochastic factor. The predators are of better stability under strong correlation of noises.