A single-chip microelectromechanical system (MEMS) capacitive microphone is designed and modeled. The mechanical model of the structure is extracted and the mathematical equations for a description of the microphone behavior are obtained. Then the proposed microphone characteristics are considered. In this structure, by adding Z-shape arms around the diaphragm, diaphragm hardness is decreased and diaphragm displacement becomes uniform. The sensitivity and the pull-in voltage are improved despite the decreasing size. The perforated diaphragm of this microphone is supported by Z-shape arms at its four corners. These arms around the diaphragm decrease the stiffness and air damping of the microphone. The behavior of this microphone is also analyzed by the finite element method. The structure has a diaphragm thickness of 2  μm, a diaphragm size of 0.32  ×  0.32  mm², an air gap of 2  μm, and a highly doped monocrystalline silicon wafer as a backplate. The proposed microphone is simulated with IntelliSuite software. According to the results, the new microphone has a sensitivity of 14.245  mV  /  Pa and a pull-in voltage of 5.83 V. The results show that the proposed MEMS capacitive microphone is one of the best structures in performance. The obtained mathematical equations for description of the microphone’s behavior have good agreement with the simulation results.