The authors consider the convergence speed of mean field annealing (MFA). They combine MFA with the microcanonical simulation (MCS) method and propose an algorithm called microcanonical mean field annealing (MCMFA). In the proposed algorithm, cooling speed is controlled by current temperature so that computation in the MFA can be reduced without degradation of performance. In addition, the solution quality of MCMFA is not affected by the initial temperature. The properties of MCMFA are analyzed with a simple example and simulated with Hopfield neural networks. In order to compare MCMFA with MFA, both algorithms are applied to graph bipartitioning problems. Simulation results show that MCMFA produces a better solution than MFA.