Data bandwidth dominates the performance and power consumption in the video encoder design. In which a low bandwidth and bandwidth aware motion estimation design enables smooth and better video quality as well as lower power consumption on data accesses. This paper proposes a bandwidth efficient motion estimation and its hardware implementation to deal with the bandwidth issues. First, an on-demand data access mechanism is proposed to acquire the reference data according to the video content for motion estimation process and thus can avoid unnecessary reference data loading. Furthermore, the available bandwidth constraint is properly modeled into our proposed rate distortion optimization framework to efficiently use the data bandwidth. Simulation results show that our proposed algorithm not only allocates proper data bandwidth for motion estimation according to video content but also saves 79.15% data bandwidth demand with 0.03 dB PSNR drop and 2.50% bitrate increase in maximum for 4 CIF resolution sequences, when compared to the fully data reuse full search motion estimation which reuses the overlapped reference data to avoid unnecessary data reloading. In addition, under the available data bandwidth constraint, our proposed algorithm can achieve 2.43%, 0.08%, and 0.20% BD-bitrate saving with 0.17 dB, 0.01 dB, and 0.01 dB BD-PSNR increase on average for high, median, and low motion sequences when compared to the full search motion estimation algorithm. The resulted design only needs 75.27 K gate counts when running at 23 MHz operating frequency for 4 CIF at 30 frames/s with 90 nm CMOS process due to its search range independent buffer design.