This paper proposed a method of optical fiber gas sensing which based on the detection of sensitive phase of light wave combined with organic polymers, simultaneously, the experimental verification was given. We found that the refractive index of the organic polymer will change accompanied with the change of concentrations of acid gases that act with the organic polymer. So, we put the organic polymer film into the optical fiber Fabry-Perot (F-P) cavity and analyze the spectral characteristics of the output of the optical fiber F-P cavity, then, we realize the hydrogen sulfide gas sensing. Experimental results show that the refractive index of organic polymer decreasing when the concentration of the gas under the test is increasing. At low concentration, a system resolution record of 3.0455 ~ 4.7777 × 10<sup>−5</sup>m/%VOL is obtained, phase sensitivity is found to be 1.94 ×10<sup>2</sup> rad/%VOL and concentration resolution is found to be 5.15 x 10<sup>-3</sup> <i>ppm</i>. Through this test, we proved the possibility by using organic polymer to realize the sensing of gas. In general, this scheme can be applied to high-precision measurement of carbon dioxide, hydrogen sulfide and other gases in the petrochemical field.