In this paper we consider a general deterministic model consisting of a micro-organism pool living on detritus of mangrove litter and its invertebrate predators. Here the growth rate of micro-organism is assumed in the general form and Holling type-II functional response of the invertebrate predators is incorporated. We find a globally attracting steady state for some parameter values, and a stable limit cycle for some other parameter values. It is also shown that there exists Hopf-Andronov bifurcation with respect to the control parameters. It is found that the specific growth rate and the food conversion efficiency rate of invertebrate predator governs the dynamics of such a model.