Solution-processable hybrid perovskite solar cells are a new member of next generation photovoltaics. In the present work, a low-temperature two-step dipping method is proposed for the fabrication of CH3NH3PbI3-xClx perovskite films on the indium tin oxide glass/poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) substrate. The bandgaps of the CH3NH3PbI3-xClx perovskite films are tuned in the range between 1.54 and 1.59 eV by adjusting the PbCl2 mole fraction (n(Cl)/(n(Cl) + n(I))) in the initial mixed precursor solution from 0.10 to 0.40. The maximum chlorine mole fraction measured by a unique potentiometric titration method in the produced CH3NH3PbI3-xClx films can be up to 0.220 +/- 0.020 (x = 0.660 +/- 0.060), which is much higher than that produced by a one-step spin-coating method (0.056 +/- 0.015, x = 0.17 +/- 0.04). The corresponding solar cell with the CH3NH3PbI2.34 +/- 0.06Cl0.66 +/- 0.06 perovskite film sandwiched between PEDOT:PSS and C-60 layers exhibits a power conversion efficiency as high as 14.5%. Meanwhile, the open-circuit potential (V-oc) of the device reaches 1.11 V, which is the highest V-oc reported in the perovskite solar cells fabricated on PEDOT:PSS so far.