We measured pseudodielectric functions in the visible-ultraviolet spectral range of Pb(ZrxTi1-x)O3 (x=0.2, 0.56, 0.82) (PZT) grown on platinized silicon substrate using the sol-gel method and also on (0001) sapphire using radio frequency sputtering method. Using a parametric optical constant model, we estimated the dielectric functions of the PZT thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard critical point model, we determined the parameters of the critical points. In the second derivative spectra, the lowest bandgap energy peak near 4 eV is fitted as a double peak for annealed PZTs associated with the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest bandgap is fitted as a single peak. We compared the bandgap energies with literature values.