We report the pulsed laser deposition (PLD) of nanocrystalline/amorphous homo-composite BaTiO3 (BTO) films exhibiting an unprecedented combination of a colossal dielectric constant (εr) and extremely low dielectric loss (tan δ). By varying the substrate deposition temperature (Td) over a wide range (300-800 °C), we identified Td = 550 °C as the optimal temperature for growing BTO films with an εr as high as ~3060 and a tan δ as low as 0.04 (at 20 kHz). High-resolution transmission electron microscopy revealed that the PLD-BTO films consist of BTO nanocrystals (~20-30 nm size) embedded within an otherwise amorphous BTO matrix. The impressive dielectric behavior is attributed to the combination of highly crystallized small BTO nanograins, which amplify interfacial polarization, and the surrounding amorphous matrix, which effectively isolates the nanograins from charge carrier transport. Our findings could facilitate the development of next-generation integrated dielectric devices.