The objective of this study is to evaluate the prediction accuracy of FDS(Fire Dynamic Simulator) for the thermal and chemical characteristics of under-ventilated fire with unsteady fire growth in a semi-closed compartment. To this end, a standard doorway width of the full-scale ISO 9705 room was modified to 0.1 m and the flow rate of heptane fuel was increased linearly with time (until maximum 2.0 MW based on ideal heat release rate) using a spray nozzle located at the center of enclosure. To verify the capability of FDS, the predicted results were compared with a previous experimental data under the identical fire conditions. It was observed that with an appropriate grid system, the numerically predicted temperature and heat flux inside the compartment showed reasonable agreement with the experimental data. On the other hand, there were considerable limitations to predict accurately the unsteady behaviors of CO and $CO_2$ concentration under the condition of continuous fire growth. These results leaded to a discrepancy between the present evaluation of FDS and the previous evaluation conducted for steady-state under-ventilated fires. It was important to note that the prediction of transient CO production characteristics using FDS was approached carefully for the under-ventilated fire in a semi-closed compartment.