Energy Harvesting (EH) technologies are getting attractive to realize the battery-less wireless sensing networks (WSNs). In EH-WSNs, opportunistic routing that the intermediate nodes relay packets is preferred due to the extremely constrained energy. However, in the conventional scheme, intermediate nodes rigidly determine its relaying slot by calculating distances between a source and a destination and this causes heavy computation for nodes. In this paper, we propose a lightweight grid-based relay slot selection scheme in EH-WSNs. In our scheme, we use square-shaped grid and divide the network virtually to give each node primitive coordination and each intermediate node decides its relaying slot by calculating the differential of grid-index between a sender and a receiver. Based on grid-based coordination, our scheme turns multiplications into lightweight subtractions and this reduces the computational complexity and required memory. In addition, we also propose a probabilistic relaying scheme to reduce collisions in each relaying slot. We evaluate the conventional and proposed schemes through the computer simulation and show that our scheme reduces the computational complexity and achieves comparable throughput to the conventional scheme.