Graph Neural Networks (GNNs) have demonstrated powerful representation capability in numerous graph-based tasks. Specifically, the decoupled structures of GNNs such as APPNP become popular due to their simplicity and performance advantages. However, the end-to-end training of these GNNs makes them inefficient in computation and memory consumption. In order to deal with these limitations, in this work, we propose an alternating optimization framework for graph neural networks that does not require end-to-end training. Extensive experiments under different settings demonstrate that the performance of the proposed algorithm is comparable to existing state-of-the-art algorithms but has significantly better computation and memory efficiency. Additionally, we show that our framework can be taken advantage to enhance existing decoupled GNNs.