An energy-time entanglement-based dispersive optics quantum key distribution (DO-QKD) is demonstrated experimentally over optical fibers of 20 km. In the experiment, the telecom band energy-time entangled photon pairs are generated through spontaneous four-wave mixing in a silicon waveguide. The arrival time of photons is registered for key generation and security test. High-dimensional encoding in the arrival time of photons is used to increase the information per coincidence of photon pairs. The bin sifting process is optimized by a three-level structure, which significantly reduces the raw quantum bit error rate (QBER) due to timing jitters of detectors and electronics. A raw key generation rate of 151 kbps with a QBER of 4.95% is achieved, in a time bin encoding format with 4 bits per coincidence. This experiment shows that the entanglement-based DO-QKD can be implemented in an efficient and convenient way, which has great potential for quantum secure communication networks in the future.