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The structure, working principle and fabrication of a humidity sensor based on carbon nanotubes (CNTs) were presented. The sensor resistance was sensitive to humidity. Schrödinger equation associated to the potential barrier between two CNTs was set up and solved. The analysis results indicated that the fluctuation of sensor resistance was caused by instability of CNTs, and the testing frequencies can change the relationship between sensor resistance fluctuating and CNTs stability. According to the experiment results, the stability was related to testing frequencies, and the fluctuating range of the sensor resistance at the testing frequency of 500Hz is about 10 times of that at 100KHz.