We have proposed a cone-shaped metal-insulator-semiconductor cathode (COSMISC) to improve the emission efficiency of the conventional metal-insulator-semiconductor cathode. This cathode is also recognized as the field emitter with prior electron acceleration mechanism. Since the COSMISC emits the electrons with higher energy than those at the Fermi level of the metal electrode, it is expected that the current fluctuation due to the change in work function of the metal electrode is less significant than that of a conventional field emitter. In this article, we analyzed the emission characteristics of the COSMISC in detail by Monte Carlo simulation, especially from the viewpoint of the emission stability against the change in work function of the upper metal electrode. The calculation procedure is as follows: electrons are generated according to their energy distribution at the semiconductor-insulator surface, and the scattering processes in the insulator and in the metal electrode were simulated with random numbers. Emission of electrons into vacuum was judged also according to the transmission probability at the surface barrier of the metal electrode. The obtained results are arranged with respect to the work function and also to the external field at the apex of the metal electrode. It was shown that the fluctuation of the emission current in COSMISC due to the change in work function is lower than that of the conventional field emitter.