We demonstrate an electrooptic synthesis technique for generating arbitrarily shaped short optical pulses from a CW narrow linewidth laser. For the optical pulse shaping, a large-amplitude electrooptic phase modulator is specially fabricated by employing the quasi-velocity-matching. The phase modulated light having sidebands as wide as 1 THz is separated and phase-only-controlled spatially by a liquid crystal modulator array. After composing the light by using a grating, nearly 1. 2 ps of Fourier-transform-limited optical pulses is obtained.