The effect of incoherent population pumping on the steady-state population inversion and the quadrature squeezing spectra produced in the resonance fluorescence of a two-level atom is investigated. In the presence of incoherent population pumping, the steady-state population inversion is increased for small frequency detuning but is not changed for large frequency detuning. For resonant excitation at low intensities, the weak incoherent pumping degrades the degree of the squeezing and shifts the position of the maximum squeezing; for off-resonant excitation at strong intensities, the weak incoherent pumping hardly changes the squeezing spectra. But when the incoherent pumping is strong the squeezing may be completely destroyed for both cases.