Tunable Fabry-Perot filter is an important device in optics. It is widely used in high resolution spectroscopy, laser linewidth measurement, laser frequency stabilization and so on. The filtering characteristics of the Fabry-Perot filter are directly related to the cavity length, and the performance is greatly influenced by the parallelism of the cavity mirrors. For a tunable Fabry-Perot filter with parallel cavity, it is difficult to directly measure the cavity length and determine the parallelism of the cavity in the tuning process. In this paper, a tunable Fabry-Perot filter with an automatic cavity-length stabilization and monitoring system is designed. Four metallic electrodes are deposited on each cavity mirror of the FP filter, thus to form 4 parallel-plate type capacitive sensors. With the help of a capacitance measurement circuit and a micro-controller circuit, the capacitances of the sensors can be acquired. After calibration, the mean value of the capacitances is used to determine the cavity length of the FP filter, while the differential capacitance values in two orthogonal directions are used to monitor the tilt of the cavity mirrors. A feedback control system composed by PZTs, a MCU and the capacitive sensors is therefore constructed to automatically stabilize the F-P cavity length and to adjust the parallelism between the cavity mirrors. The automatic cavity-length stabilizing and monitoring system has the advantages of high accuracy, strong disturbance resistance and high measuring speed. Experimental results prove that it can effectively measure the cavity length of the tunable Fabry-Perot filter, and can stabilize the FP filter as well.