In this study, predator-prey relations of a food web are investigated when two species face harvesting in the food web. A food chain model built on ordinary differential equations is used to investigate such a food web. After ensuring the existence of a solution for the food chain model, all the possible equilibrium points are found and investigated. Then, the stability analysis of important equilibrium points is numerically made. After capturing important values of harvest rates for a sustainable fishery, the predator-prey system is investigated under different levels of harvesting. This investigation shows us how important stability analysis is to controlling fish stocks and capturing sustainable fisheries.