X-ray Talbot-Lau interferometer has been used most widely to perform X-ray phase-contrast imaging with a conventional low-brilliance X-ray source, it yields high-sensitivity phase and dark-field images of sample producing low absorption contrast, thus bearing tremendous potential for future clinical diagnosis. In this manuscript, while changing accelerating voltage of the X-ray tube from 35KV to 45KV, X-ray phase-contrast imaging of a test sample were performed at each integer KV position to investigate the characteristic of an X-ray Talbot-Lau interferometer (located in the Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Japan) vs. tube voltage. Experimental results and data analysis show that this X-ray Talbot-Lau interferometer is insensitive to the tube accelerating voltage within a certain range, fringe visibility around 44% is maintained in the aforementioned tube voltage range. This experimental research implies that potential new dual energy phase-contrast X-ray imaging strategy and rough refraction spectrum measurement is feasible with this X-ray Talbot-Lau interferometer.