We report the measurement of photoexcitation cross-sections of three first-step uranium transitions $(0 \rightarrow 16900.38$ cm^-1 , $0 \rightarrow 17361.89$ cm^-1 and $620 \rightarrow 17361.89$ cm^-1) using saturation method. These measurements were performed on a resonance ionization mass spectrometry (RIMS) set-up consisting of Nd:YAG-pumped dye lasers, a reflectron time-of-flight mass spectrometer and high-temperature atomic vapour source. The uranium vapours were excited and photoionized by two-colour, three-photon photoionization scheme using Nd:YAG-pumped dye laser system. The resultant photoion signal was monitored as a function of dye laser fluence used for first step excitation to measure the excitation cross-section values. A new approach was adopted to overcome the large uncertainties associated with such measurements. With this approach the cross-section of transitions whose value is already reported in the literature was measured as a bench mark. By normalizing the measured value to the reported value, a scaling factor was derived. This scaling factor was used to scale up the cross-section values of other transitions measured by this method.