When adapting the transmitter to the channel state information (CSI), improved transmission is possible compared to the open loop system where no CSI is provided at the transmitter. However, since the perfect channel information is rarely available at the transmitter, the system design based on the partial CSI becomes an important factor. Especially, in mobile environments, the consideration for the outdated CSI should be applied for mitigating the performance degradation. In this paper, we propose a robust adaptive modulation and coding scheme for bit-interleaved coded orthogonal frequency division multiplexing over time-varying channels. With reasonable feedback overhead, the proposed scheme shows the enhanced performance by compensating for the outdated CSI due to Doppler spread. Simulation results confirm that the performance gain is achieved by applying an accurate BER estimation method.