A fiber-optic Michelson interferometer based on a photonic crystal fiber (PCF) is proposed, constructed by fusing a piece of PCF and a single-mode fiber (SMF). The taper between the SMF and the PCF works as a coupler. It excites the high-order cladding modes and couples the fundamental mode of the core and high-order cladding mode after being reflected by the end face of the PCF to form an intermodal interference. Since all the air holes in the PCF are exposed to the environment, the moisture and the fiber are fully affected, effectively improving the sensor's humidity sensitivity. The experimental results show that the humidity sensitivity of the designed sensor is -0.095 dB/% with a linearity of 0.998 in a 30%-90% relative humidity range. The temperature sensitivity is 0.008 nm/℃ with a linearity of 0.997 from 20 ℃-100 ℃, and error in the humidity measurement, caused by temperature, is 0.01%/℃. The stability experiment indicates a humidity standard deviation of 0.25%, and the human breathing test shows a sensor response time of 190 ms. Importantly, the designed sensor has a simple structure, high sensitivity, good stability, fast response time, and is easy to fabricate, indicating excellent potential in humidity detection applications.