Temporal characterization of femtosecond optical pulses produced in a Kerr-lens mode-locked Ti:sapphire laser is performed using a multi-shot second-harmonic-generation frequency-resolved optical gating (FROG) technique. The FROG apparatus is suited for the characterization of the low-energy sub-10-fs laser pulses with a high repetition rate. The performance of the FROG apparatus is tested through the characterization of relatively long laser pulses with Gaussian spectra. The characterization of a 16.6-fs Gaussian laser pulse and a positively chirped pulse are proved to be successful through the self-consistency check of FROG measurement. The measured pulse duration of laser pulses with broad spectrum generated in a mirror-dispersion-controlled Ti:sapphire laser is 8.6 fs, which is 0.7 fs larger than that of transform-limited laser pulse. In the measurement of the sub-10-fs laser pulses, the discrepancy between a FROG marginal and the auto-convolution of the laser spectrum is observed in the long-wavelength part. This self-consistency check shows that the main cause of this discrepancy comes from the wavelength dependence of the quantum efficiency of the detector in the FROG apparatus. Even though the measurement of the laser phase has some error due to this problem, the measured pulse duration is found to be correct through a cross-check using an interferometric autocorrelation measurement coupled with an electric-field reconstruction algorithm. The FROG apparatus fabricated in the work can be reliably used for the temporal characterization of high-repetition-rate femtosecond laser pulses.