The Smart Grid (SG) is one of the latest emerging and rising models for modernizing traditional electrical power grids, and wireless communication is considered as a major building block in realizing SG. SG applications enable electrical devices to be interconnected and communicate with each other, requiring pervasive control of these actors. Therefore, wireless sensor network-based applications are well suited to this requirement. This paper proposes an energy-efficient neighbor discovery protocol for 6LoWPAN SG applications. We discuss some practical challenges and difficulties in applying block designs to 6LoWPAN neighbor discovery problems and provide a new solution to the discovery problem derived from the original block designs. In this proposed approach, we design a new construction mechanism of neighbor discovery schedules and provide a mathematical proof of the proposed concept. A key aspect of the proposed protocol is that it combines any two block designs in order to overcome limitations of the original block designs. In the simulation study, we evaluate the performance of the proposed protocol and compare its performance with that of existing representative neighbor discovery protocols using TOSSIM. The results of our simulation study show that the maximum latency of the proposed protocol is about 40% lower than that of existing protocols. Furthermore, our protocol spends approximately 30% less energy than existing protocols during the neighbor discovery process.