We consider the mathematical model of a resource-based autotroph-herbivore system where diffusion of nutrient within the soil is taken into account. We have derived the conditions for the existence of steady-state to the system and studied the stability and instability of the patially homogeneous case. Then we have introduced the diffusion term to the system and studied the qualitative behabviour of the spatially inhomogeneous case. Finally we have discussed the salient features of the analytical results giving also the ecological interpretations.