The widespread deployment of Internet of Things (IoT) devices brings more and more computation intensive or delay sensitive tasks, causing a series of challenges to efficient services. Collaborative edge computing is an effective way to solve them, where the tasks will be processed in the devices, edge servers, and cloud server in parallel. However, the above collaborative paradigm requires dense deployment of base stations (BSs) and consumes lots of energy. To address this problem, in this paper, we introduce energy harvesting technology and construct a collaborative edge computing system powered by hybrid energy. Considering the highly variable task execution delay caused by the resource contention and the unstable energy state, we further introduce the Holt Linear Exponential Smoothing Prediction to predict the delay and then propose an Online Server Control schedule called OSC based on Lyapunov optimization to obtain the optimized offloading decision without the knowledge of the future system state. The extensive simulations illustrate that the proposed OSC outperforms other benchmark ones.