In recent years, marine exploration has become one of the most popular research subjects. At present, gliders in Underwater Acoustic Sensor Networks (UASNs) are equipped with a variety of sensors, which can play an important role in marine detection and monitoring. In addition, gliders also have the ability of data collection and storage. When coexisting with the sensor nodes, they can be regarded as special sensor nodes with semi-determined sawtooth trajectories. In hybrid UASNs including sensor nodes and gliders, a robust routing protocol is required to improve the poor network connectivity caused by long transmission delay, high bit error rate and unreliable transmission links. In this paper, the Fuzzy Logic Algorithm (FLA) is used to convert multiple input parameters into one output value, thus reducing the storage burden of the network. Therefore, a glider-assist routing scheme with trajectory prediction is proposed to improve the connectivity of the hybrid network. The simulation results show that our scheme is superior to other protocols in terms of delivery ratio, end-to-end latency and lifetime.