The basic theory of dispersion compensation of the thin film is discussed. The optimized multiplayer mirrors used for a femtosecond mode-locked Ti∶Sapphire laser is reported. The mirrors exhibit high reflectivity (>99.5%) over a wavelength range from 720 to 870 nm, high transmittance (>90%) from 510 to 550 nm and smooth variation of group delay dispersion from 740 to 850 nm. Most GDD of a 5-mm Ti∶Sapphire crystal can be compensated by seven bounces.