A scheme of the large frequency shift for high-order harmonic generation (HHG) produced by atomic gas driven by an asymmetric laser pulse is proposed in the tunneling ionization regime. By numerically solving the three-dimensional time-dependent Schrodinger equation in the dipole approximation, we theoretically investigate the characteristics of HHG emitted from hydrogen atom driven by the laser pulse with different rising and falling times. Our results show that the HHG spectra of atomic H in cutoff region present a strong redshift and blueshift. The shift can be adjusted by varying the rising time or falling time of the laser pulse. The time frequency analysis, reveals that the reason for the frequency shift comes from different contributions from the rising time or falling time in the asymmetric laser pulse. If the contributed harmonics during the falling time is larger than that during the falling time, the red shift of HHG occurs. otherwise the blue shift appears. Therefore, by shaping the laser pulse waveform, the frequency of atomic HHG for a given order in the cutoff region in the tunneling ionization regime is tunable, which can cover the frequency range from the odd order to the adjacent even order.