In this paper, we present a prey-predator fishery model with two zonal environment (unreserved and reserved) in which the unreserved zone is accessible to both prey and predator and the other is accessible only to the prey. Harvesting of the prey is permitted only in the unreserved zone. The authoritarian agency of the fishery has power over the exploitation by a striking tax per unit biomass of the prey. The interior steady state of the model is identified. The local and global stabilities of the interior steady state are studied using the Routh-Hurwitz's and Lyapunov's methods respectively. The optimal harvesting scheme is being discussed using Pontryagin's maximum principle. The effect of Gaussian white noise on stability is analyzed by estimating the population variances. Some numerical simulations are carried out through the MATLAB. © 2015 Academic Publications, Ltd.