We report a compact in-fiber Mach-Zehnder interferometer (MZI) made along a hollow-core photonic bandgap fiber (HC-PBF). The MZI uses a long period grating (LPG) and an offset-splice joint (OSJ) which act as beam splitter and combiner respectively. The LPG was produced by use of a high frequency pulsed CO2 laser, and the OSJ was made in serial with the LPG by using a commercial fusion splicer. The interference is between the fundamental core mode (FCM) and a high-order core mode (HOCM). The proposed interferometer was experimentally tested for temperature and strain measurements, and the sensitivities of the interference fringe dip wavelength to temperature and strain are 107.5 pm/ (°C-m) and -1.24 pm/με, respectively.