The mixed fleet heterogeneous dial-a-ride problem (MF-HDARP) consists of designing vehicle routes for a set of users by using a mixed fleet including both heterogeneous conventional and alternative fuel vehicles. In addition, a vehicle is allowed to refuel from a fuel station to eliminate the risk of running out of fuel during its service. We propose an efficient hybrid adaptive large neighborhood search (hybrid ALNS) algorithm for the MF-HDARP. The computational experiments show that the algorithm produces high quality solutions on our generated instances and on HDARP benchmarks instances. Computational experiments also highlight that the newest components added to the standard ALNS algorithm enhance intensification and diversification during the search process.