Recent progress in optical fiber Mach-Zehnder interferometers (MZIs) has gained many achievements in sensing application. However, the strain sensitivity of optical fiber MZIs is low due to the low elasto-optical coefficient of silica. In this Letter, we propose and demonstrate a method to modulate the guided modes in an MZI based on a special hollow core microstructured optical fiber (HCMOF) by fabricating periodical deformations. Specifically, periodical deformations reduce the extinction ratio of the transmission spectrum. Furthermore, the axial tension modulates these periodical deformations, leading to the enhanced strain sensitivity in comparison to the configuration without deformations. In our experiment, the strain response from 0 to 1000µε is obtained with a sensitivity of 0.00359dB/µε corresponding to an improvement of 13 times compared with a sensor based on same HCMOF without deformations.