Solid-state hydrogen storage is considered to be the most promising hydrogen storage technology because of its high volumetric capacity and good security. The process of hydrogenation and dehydrogenation of solid hydrogen storage materials can be characterized by a diffusion kinetic model, which can be used to guide the safe and efficient application of hydrogen storage materials. Currently, experimental study on the dehydrogenation characteristics under constant pressure outer boundary condition has not been carried out methodically, and a simple and reliable diffusion kinetic model under this condition should be established based on the experimental results. In this study, an experimental platform for hydrogen absorption and constant pressure dehydrogenation of solid hydrogen storage materials was independently established. The TiMn1.5 alloy and its interstitial hydrides were taken as the experimental research objects to conduct constant pressure dehydrogenation tests, and the dehydrogenation properties at different temperatures were systematically studied. The results show that the dehydrogenation rate decreases with the increase of testing time. The ultimate capacity of hydrogen release increases first and then decreases with the increasing temperature, reaching the maximum value at 30 °C. It is found that the diffusion coefficient increases linearly with time during constant pressure dehydrogenation process. On this basis, a linear diffusion kinetic model is established. The initial diffusion coefficient D0 calculated by the new model has a quadratic polynomial relationship with temperature, and the increase coefficient α of diffusion coefficient has a linear relationship with temperature. According to the mathematical expressions, the dehydrogenation process of TiMn1.5 alloy at different temperatures can be predicted. The research results can provide theoretical guidance for the safe, efficient and controllable application of hydrogen storage materials.