In this letter, we propose a joint channel and queue-aware resource block allocation algorithm for the long-term evolution (LTE) downlink based on buffer overflow probability estimation. To this end, we first derive an equation for the buffer overflow probability bound. Furthermore, we propose a novel service curve in order to estimate maximum delay for LTE system users considering the Effective exponential signal-to-noise ratio mapping to the SNR values of the LTE sub-bands. Simulation results reveal that in general, compared to other approaches, the proposed scheduling algorithm provides lower delay and buffer overflow rate while maximizing throughput.