Quantum dot-cavity coupling systems is investigated by using quantum master equation. In order to illustrate theory mode, we analyze a strong coupling (SC) experiment in quantum dot-microcavity system. After studying, we find that the pump in the coupling system yieds new criteria to achieve SC with a steady state, where the incoherent pump hinders or favors SC. Double-peak structure of cavity-emitted spectrum is not an unequivocal signature of strong coupling, which dependes on the incoherent pump. Research shows that SC often appears in disguise of a single peak and double peak in the weak coupling (WC) emission spectrum which closely relates to the parameter values controlled in the system. The spectral shape of the cavity emission changes from double peak to single broad peak then to narrow single peak again with increasing exciton pumping. The cavity-emitted spectra characterized in double-peak experience transition from the SC to WC when the cavity decay rate is increasing. The effective coupling strength of the quantum dot-cavity detuning system relates with incoherent pump closely.