High dielectric CaCu3Ti4O12 (CCTO) thin films were epitaxially grown on (001) LaAlO3 (LAO) substrates by pulsed laser deposition. Microstructural studies by x-ray diffraction, pole figure measurements, and transmission electron microscopy show that the as-grown films are good single crystalline quality with an interface relationship of (001)CCTO//(001)LAO and [100]CCTO//[100]LAO. Dielectric property measurements show that the films have an extremely high dielectric constant with value of 10 000 at 1 MHz at room temperature. It is interesting to note that the twinned substrate results in the formation of twinning or dislocations inside the CCTO film.