Highly (h00)-oriented (Ba, Sr)TiO$_3$(BST) thin films were grown by pulsed laser deposition on the perovskite LaNiO$_3$(LNO) metallic oxide layer as a bottom electrode. The LNO films were deposited on SiO$_2$/Si substrates by rf-magnetron sputtering method. The crystalline phases of the BST film were characterized by x-ray $ heta$-2$ heta$, $omega$-rocking curve and $psi$-scan diffraction measurements. The surface microsturcture observed by scanning electron microscopy was very dense and smooth. The low-frequency dielectric responses of the BST films grown at various substrate temperatures were measured as a function of frequency in the frequency range from 0.1 Hz to 10 MHz. The BST films have the dielectric constant of 265 at 1 kHz and showed multiple dielectric relaxation at the low frequency region. The origin of these low-frequency dielectric relaxation are attributed to the ionized space charge carriers such as the oxygen vacancies and defects in BST film, the interfacial polarization in the grain boundary region and the electrode polarization. We studied also on the capacitance-voltage characteristics of BST films.