An optical fiber evanescent wave methane gas sensor based on core diameter mismatch is reported. The sensor consists of a multimode fiber in which a short section of standard single-mode fiber, coated with the inclusion of cryptophane molecules E in a transparent polysiloxane film, is inserted. The sensing principle is analyzed by optical waveguide theory. For different sensing film thicknesses and interaction lengths, the sensor signal is investigated within the methane concentration range of 0-14.5% (v/v). It is shown that the sensor signal with the thickness of 5 \mu m and the interaction length of 3 mm strengthens linearly with the increasing concentration of methane, with a slope of 0.0186. The best detection limit of the sensor for methane is 2.2% (v/v) with a response time of 90 s. This sensor is suitable for the detection of methane concentration below the critical value of 5%.