Integrated growth of pervoskite functional oxide films with Ⅲ-Ⅴ semiconductor GaN due to its potential applications in various devices was explored in this letter.Some typical dielectrics such as SrTiO3,Bi4Ti3O12 (BTO) and Pb(Zr0.52Ti0.48)O3 (PZT)thin films were fabricated on GaN by Laser-MBE through MgO or TiO2 buffered method.It was found that dielectric thin films were highly epitaxiaily grown on GaN substrates by insertion of a few nanometer thick bufferlayer,The epitaxial relationship of the heterostructures was determined by reflective high energy electron diffractions (RHEED),X-ray diffraction (XRD) and high resolution transmission microscope (HRTEM).Electrical measurements demonstrate that favorable electrical performance for dielectric films can be obtained,for example,the non-c axis BTO films possess a large remnant polarization (2Pr=45μC/cm2).Meanwhile the mobility and carrier concentration for semiconductors can be maintained.Additional the mobility of 2DEG in AlGaN/GaN was increased by around 30% after Al2O3 dielectric film were deposited.Our results would provide a possible way to realize all-in-one multifunction and hereto-interface modulation effects by dielectrics/GaN heterostructures.