Monitoring and transforming smart grid (SG) assets in a timely manner is highly desired for emerging smart grid applications. This critically requires the design of a neighborhood area network (NAN) which is capable of providing high-efficiency and reliable two-way last mile communication from meters to other SG domains. For this demand, IEEE 802.11s based wireless mesh network (WMN) is anticipated to be utilized in a NAN as it can provide high scalability, high-speed and cost-effective wireless transmission. In this paper, we propose a NAN QoS-aware and load-balance routing scheme (NQA-LB) based on the default hybrid wireless mesh protocol (HWMP) of IEEE 802.11s, which aims to address multiple QoS requirements from different NAN applications, and guarantee the highly reliability transfer of NAN traffic data towards gateway. With the NQA-LB, various QoS requirements can be satisfied through sufficient differentiated services as well as network congestion is mitigated by achieving load balance between multiple transmission paths. In order to improve the reliability of NQA-LB, we present an EDCA based adaptive priority adjustment scheme, called AP-EDCA, which dynamically adjusts packet's priority to increase the throughput under low load condition and to mitigate the collision under heavy load condition to improve the reliability of applications with high QoS requirements. Extensive simulation experiments demonstrate the superiority of the proposed scheme in terms of packet delivery ratio, end-to-end delay and throughput while satisfies various QoS requirements much better at the same time.