Compositionally graded (Ba1−xSrx)TiO3 (BST) thin films (with 0.0 ⩽ x ⩽ 0.25) were grown by pulsed laser deposition on the (100)MgO single-crystal substrates covered with a conductive La0.5Sr0.5CoO3 (LSCO) layer as a bottom electrode. Their epitaxial growth, dielectric response, and microstructure were characterized. The epitaxial relationships between the BST, LSCO, and MgO can be determined as BST//LSCO//MgO and (100)BST//(100)LSCO//(100)MgO, from the x-ray diffraction (rocking curve, ϕ scans) and electron-diffraction patterns. Dielectric data showed that the room temperature values of the dielectric constant and dielectric loss of the graded BST films were 630 and 0.017 at 100 kHz, respectively. Cross-sectional transmission electron microscopy (TEM) images reveal that both the BST films and the LSCO bottom electrode grow with a columnar structure, and they have flat interfaces and overall uniform thickness across the entire specimen. Cross-sectional high-resolution TEM images reveal that at the LSCO/MgO(100) interface, an interfacial reaction is not seen, whereas edge-type interfacial dislocations with their extra half-planes residing in the LSCO side are observed with an average interval of 2.20 nm, close to the theoretical value of 2.15 nm. At/near the LSCO/BST interface, the graded BST films grow perfectly and coherently on the LSCO lattice because they have the same type of crystal structure and almost same lattice constants, and no interfacial dislocations are observed. Planar TEM images show that the graded films exhibit granular and/or polyhedral morphologies with an average grain size of 50 nm, and the aligned rectangular-shaped voids were also observed. High-resolution TEM images show that the length sizes of voids vary from 8 to 15 nm, and with width of 5 to 10 nm along the 〈001〉 direction in the (100) plane.