The coral symbiotic algae zooxanthellae is often expelled from the host as the host coral is under physiological stress, causing the coral to turn completely white. Such coral bleaching events are occurring more frequently with the increase in the global warming, ocean acidification and increased level of anthropogenic impacts such as eutrophication. In the present study, we investigated the effects of inorganic nutrients including ammonium, nitrate, phosphate and elevated water temperature on the symbiotic zooxanthellae density in the fragment of branching coral Acropora nobilis. Zooxanthellae density in the host coral decreased 8 hrs after the experiment at a given elevated water temperature ($32^{circ}C$, p < 0.05). In contrast, no clear coral bleaching or decrease in the symbiotic algae density was observed from the branching coral exposed to a normal water temperature of $30^{circ}C$ and high levels of nutrients such as 20 ${mu}M$ of $NH_4Cl$, 20 ${mu}M$ of $NaNO_3$ and, 10 ${mu}M$ $KH_2PO_4$. Accordingly, the data indicated high water temperature is one of the stressful factors to cause bleaching in A. nobilis, whereas the high levels of nutrients is not a factor. It is believed that the results obtained in the present study are useful as baseline information in the management of the coral reefs.