Due to the unique optical properties of low loss, low nonlinearity, high threshold and low latency, hollow core bandgap fibers are endowed with high expectations in the field of high power delivery, optical fiber communication, nonlinear optics, fiber sensors, etc. Fiber dispersion, as one of the basic transmission characteristics of optical fiber, makes the light pulse broadened during transmission, thus has adverse effects on high power pulse transmission system and high speed optical communication system. Therefore, it is significant to study the dispersion characteristics of the hollow core bandgap fiber for its applications in the field of high power pulse transmission and high speed communications. Because of the simple structure of measurement system, low cost, high accuracy and relatively short length of fiber (just needing a few meters long), interferometric technique is suitable for dispersion measurement of hollow core photonic bandgap fiber. The key to obtaining the dispersion results with interferometric technique is the phase extractiton from the interferogram. In order to meet the requirements of hollow core bandgap fiber for wide bandwidth, high efficiency and high accuracy dispersion measurement, a novel phase extraction method based on interferometry is proposed in this paper, by which the precision of dispersion measurement is improved through using the whole data-set in the interferogram. Combining with the determinations of the peak and center of symmetry points, the extraction of phase information can be implemented directly from the interferogram. The experimental results of measuring a standard single mode fiber indicate that the difference between the experimental measurement and theoretical simulation is just 0.6 psnm-1km-1, which proves that this proposed method possesses high accuracy and is suitable for the measurement of hollow core bandgap fiber. Consequently, according to the proposed phase extraction method, the measurement system based on Mach-Zehnder interferometer is set up and the dispersion measurement of a 19 cell hollow core bandgap fiber with a core diameter of 26 m is carried out. Experimental results indicate that the fundamental mode dispersion curve of the 19 cell hollow core photonic bandgap fiber in a wavelength range from 1400 nm to 1630 nm can be obtained. Moreover, four high order mode dispersion curves are obtained for the first time. The measurement results are in accordance with the simulation results. These findings are of significant importance for exploring the dispersion characteristics of hollow core photonic bandgap fibers, and also conducible to their applications in the fields of high power laser delivery, high capacity data communications, optical fiber nonlinear, etc.