Intra-day economic dispatch of an integrated microgrid is a fundamental requirement to integrate distributed generators. The dynamic energy flows in cogeneration units present challenges to the energy management of the microgrid. In this paper, a novel approximate dynamic programming (ADP) approach is proposed to solve this problem based on value function approximation, which is distinct with the consideration of the dynamic process constraints of the combined-cycle gas turbine (CCGT) plant. First, we mathematically formulate the multi-time periods decision problem as a finite-horizon Markov decision process. To deal with the thermodynamic process, an augmented state vector of CCGT is introduced. Second, the proposed VFA-ADP algorithm is employed to derive the near-optimal real-time operation strategies. In addition, to guarantee the monotonicity of piecewise linear function, we apply the SPAR algorithm in the update process. To validate the effectiveness of the proposed method, we conduct experiments with comparisons to some traditional optimization methods. The results indicate that our proposed ADP method achieves better performance on the economic dispatch of the microgrid.