Considering the high-temperature thermosetting chemical issues in the manufacturing process of composite tensile armor layers, the curing kinetics of T700/epoxy prepregs were explored. Through differential scanning calorimetry (DSC) analysis and the Starink method, the autocatalytic reaction curing kinetic parameters were accurately calculated. Then a curing kinetic model was established. It has been shown by experimental results that the reaction rate of the prepreg is significantly increased at higher heating rates. After the peak is reached, the reaction rate is decreased more rapidly, resulting in a lower average final reaction heat. The apparent activation energy of the curing reaction for this prepreg is 77.04 kJ/mol, and high consistency with the experimental data is exhibited by the constructed curing kinetic model.