Nucleation and growth of epitaxially grown lead zirconium titanate (PZT) thin films on as-cleaved MgO(100) substrate were studied with X-ray diffraction and atomic force microscopy using a tapping mode. The films were grown by MOCVD at different deposition times from 10 to 1800 s at 650 degrees C. At the initial stage of the film deposition, the growth of layer-like PZT thin film was observed up to thickness of 1.0-1.2 nm, which corresponds to 5-6 monolayers (ML) of PZT. The chemical composition of initial layer was stoichiometric PZT. Over the thickness, formation of island structure was observed at thickness of around 2 nm. Then coalescence of three dimensional nuclei to form monodispersed grain size distribution via bimodal distribution and grain growth proceeds not only perpendicular but also horizontal to the substrate with increasing deposition time. This indicates that the growth mechanism coincides with Stranski-Krastanov (SK) growth mode. It was also clarified that the grain size distribution corresponds to the root mean square (rms) roughness on the preparation of thin film. The critical thickness of PZT thin film on MgO(100) substrate was 1.0-1.2 nm in good agreement with other reported epitaxial grown thin films.