For random access (RA) procedure in LTE-based systems, timing advance (TA) value is included for a device to adjust its uplink timing synchronization. In this letter, we propose a simple prioritized energy-efficient RA (EERA) scheme for stationary Internet of Things networks by utilizing TA value. We analyze the collision probability and average energy consumption to show the effectiveness of the EERA scheme. Performance evaluation shows that the proposed EERA scheme not only has lower collision probability but also consumes less energy than other RA schemes under practical simulation environments.