The effects of gain narrowing and high order dispersions on the pulse duration in our kilohertz chirped-pulse amplification system have been compensated experimentally. Using an acousto-optic programmable dispersive filter (AOPDF), the spectral full-width at half-maximum (FWHM) is expanded from 30 to 50 nm. Stable laser pulses with the duration of 30 fs (FWHM), which is 1.07 times Fourier-transform-limitation, have been acquired by pre-compensating the high order phase distortions using the phase measured by spectral phase interferometry for direct electric-field reconstruction (SPIDER).