By numerically solving the time-dependent Schrödinger equation for helium atoms in a single mid-infrared laser field, we explore the frequency-chirping effect of laser field on high-order harmonic and isolated attosecond pulse generation. One or two ultrabroad supercontinuum harmonic plateaus can be controlled through modulating the laser field frequency by a small time-dependent signal. Under the best chirping condition, an ultrashort 2.2 as pulse can be obtained by Fourier transformation with the bandwidth of 782 eV. Furthermore, we explain the harmonic generation physical mechanisms by classical ionizing and returning energy maps and time–frequency analyzes.