Ba0.8Sr0.2TiO3 (BST) thin films and Ba0.8Sr0.2TiO3/ZrO2 heterostructured thin films have been successfully fabricated on Pt/Ti/SiO2/Si substrates by a sol-gel process. The dielectric properties of these films were measured as a function of temperature in the frequency range of 1 kHz to 1 MHz. It is clearly observed that the dielectric peaks exist and shift to high temperature with the increase of frequency indicating the presence of relaxor-type behavior in the films. Also it is seen that one dielectric peak is observed in single layer BST thin films whereas two dielectric peaks are observed in BST/ZrO2 heterostructured thin films due to the presence of two dielectric layers having different band gap energies. The variation of peak temperature Tm, corresponding to dielectric loss maximum, with frequency and fitting to Arrhenius law gives activation energy of 1.24 eV which is very close to the activation energy of oxygen vacancies in BaTiO3. Hence, oxygen vacancies are the active defects which are contributing to the relaxation process in these films.