We have constructed a new general model of three-species food web with environmental noise by extending a simple three-species food chain model with omnivory. With this general model, the dynamical behavior of each population in four typical three-species food web structures has been numerically simulated and analyzed. We have examined how a noise signal is propagated through a food web and the responses of web components to noise; how these responses are dependent on food web structure and some possible intrinsic ecological mechanisms of noise response. The simulation results demonstrate that food web structure has significant influence on the responses of the web components to noise. The response strength depends not only on the direct influence of environmental noise but also on where a population is positioned and how it is connected to other populations in the web. So starting from relatively complex food web, the importance of web structure for the expected response of all parts of the web to noise signals could be revealed, via numerical simulation analysis on a general model of food web. This paper also implies that the responses of populations in a food web to environmental noise are determined by environmental noise, internal dynamics, and the basic food web structure in which the populations are embedded.