Underwater acoustic sensor network (UASN) is a promising technique, which will facilitate a wide range of aquatic applications. However, because of adverse underwater environments, UASN faces grand challenges and problems such as limited bandwidth, node movement, long propagation delay, three-dimension deployment, energy-constraint, expensive manufacture and deployment costs. In order to address these problems and challenges, in this paper we propose an adaptive hop-by-hop vector-based forwarding routing protocol on the basis of HH-VBF (called AHH-VBF). Firstly, during the transmission process, the radius of virtual pipeline is adaptively changed hop by hop to restrict the forwarding range of packets so that the transmission reliability can be guaranteed effectively in the sparse sensor region and the duplicated packets can be reduced in the dense sensor region; secondly, the transmission power level is also adaptively adjusted hop by hop in cross-layer fashion so that the energy-efficiency can be improved effectively; thirdly, forwarding nodes are selected based on the distance from current node to destination node so that the end-to-end delays are reduced effectively. Eventually, we propose two metrics: propagation deviation factor and effective neighbor number, to evaluate the network performance of AHH-VBF. We conduct extensive simulations using ns-3 simulator and perform theoretical analyses to evaluate the network performance. Our experimental results verified that the AHH-VBF routing protocol outperforms HH-VBF protocol, naïve Flooding and RDBF in terms of energy efficiency, end-to-end delay and data delivery ratio.