The effects of high-order harmonic generation on different chirps have been investigated using the laser waveform control modulated by chirped pulse. The results show that when using the symmetric-mid-chirped pulse, the extension of harmonic cutoff and spectral continuum come from the middle part of the laser field. However, when using the asymmetric-down-chirped pulse, the extension of harmonic cutoff and spectral continuum stem from the falling part of the laser field. Although the harmonic cutoffs from different chirped pulses can be extended, the intensity of spectral continuum from asymmetric-down-chirped pulse is two orders of magnitude higher than that from the symmetric-mid-chirped pulse. With the superposition of harmonics on the spectral continuum, two single attosecond pulses with a pulse width of 38 as can be obtained. Moreover, the intensity of attosecond pulse obtained from the asymmetric-down-chirped pulse is two orders of magnitude higher than that from the symmetric-mid-chirped pulse.