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The output incoherent spectrum and the photon blockade for the two-photon near-resonant excitation are numerically investigated by using the modified theories which are valid for an arbitrary degree of the qubit-cavity interaction. Owing to the effects of strong coupling of the system, the relaxation coefficients of the system are very sensitive to the coupling strength between the qubit and the cavity mode, which results in the redistribution of the populations and the appearance of the population inversion between the ground state and the first excited state, and it is demonstrated by the intensity of the output incoherent spectrum. The redistribution of the populations leads to one cascaded decay channel being weakened and the other possibly being enhanced significantly. Moreover, by adjusting the detuning between the qubit and the cavity mode, the phenomenon of the intercrossing in the energy levels appears. Through choosing the proper two-photon near-resonant excitation of the externa) classical driving field, the strong-coupling qubit-cavity system effectively causes one cascaded decay channel to realize the two-photon blockade. It is shown that the two-photon blockade can be further enhanced by one cascaded decay channel.