In this paper, the effects of equivalence ratio and solid propellant composition on the ignition delay time of fuel-rich mixture in solid rocket scramjets were experimentally investigated for the first time. The experiments simulated a flight condition with Mach number 5.5 at 23 km. The equivalence ratio was studied in the range of 0.39–0.58, and three different solid fuel-rich propellants were used. The experimental results show that the ignition delay time of fuel-rich mixture decreases with increasing equivalence ratio under the studied conditions. This is because that the mass flow rate and momentum of the fuel-rich mixture are increasing with the equivalence ratio, and the primary combustion in the gas generator is more efficient with the higher value of equivalence ratio. Additionally, the solid propellant composition also plays an important role in influencing the ignition delay, which may be closely related to the temperature and composition of the fuel-rich mixture, with the temperature believed to be the more critical factor. Compared with hydrocarbon-based propellant, the ignition delay when using boron-based propellant is shorter. These conclusions will provide helpful guidance for shortening the ignition delay of fuel-rich mixture in solid rocket scramjets.