It has been shown that quantum coherence induced by incoherent light can increase the efficiency of solar cells. Here we evaluate the effect of such coherence in the intermediate band solar cells. We first examine a six-level quantum IBSC model and demonstrate by simulation that the maximum of output power in a solar cell with quantum structure increases more than 16 percent in the case of coherence existence. We then propose an IBSC model which can absorb continuous spectra of sunlight and show that the quantum coherence can increase the output power of the cell. For instance, calculations indicate that the coherence makes an increase of about 31% in the maximum output power of a cell that the width of the conduction and intermediate bands are 100 and 10 meV, respectively. Also, our calculations show that the quantum coherence effect is still observed in increasing the solar cell power by expanding the width of the conduction band, although the output power is reduced due to increase in the thermalization loss. However, expanding the width of the intermediate band reduces the coherence effect.