In this paper, we apply a model predictive control based scheme to the energy management of networked microgrid ， which is reformulated based on column generation. Although column generation is effective in alleviating the computational intractability of large-scale optimization problems, it still suffers from slow convergence issues, which hinders the direct real-time online implementation. To this end, we propose a graph neural network based framework to accelerate the convergence of the column generation model. The acceleration is achieved by selecting promising columns according to certain stabilization method of the dual variables that can be customized according to the characteristics of the microgrid. Moreover, a rigorous energy management method based on the graph neural network accelerated column generation model is developed, which is able to guarantee the optimality and feasibility of the dispatch results. The computational efficiency of the method is also very high, which is promising for real-time implementation. We conduct case studies to demonstrate the effectiveness of the proposed energy management method.