Routing is still a challenging issue for wireless sensor networks (WSNs), in particular for WSNs with a non-uniform deployment of nodes. This paper introduces a Node Aggregation Degree-aware Random Routing (NADRR) algorithm for non-uniform WSNs with the help of two new concepts, namely the Local Vertical Aggregation Degree (LVAD) and Local Horizontal Aggregation Degree (LHAD). Our basic idea is to first apply the LVAD and LHAD to determine one size-proper forwarding region (rather than a fixed-size one as in uniform node deployment case) for each node participating in routing, then select the next hop node from the size-proper forwarding region in a probabilistic way, considering both the residual energy and distribution of nodes. In this way, a good adaptability to the non-uniform deployment of nodes can be guaranteed by the new routing algorithm. Extensive simulation results show that in comparison with other classical geographic position based routing algorithms, such as GPSR, TPGF and CR, the proposed NADRR algorithm can result in lower node energy consumption, better balance of node energy consumption, higher routing success rate and longer network lifetime.