We investigate the carrier envelope phase (CEP) effects on high-order harmonic generation (HHG) in ultrashort pulses with the pulse duration 2.5fs when the laser intensity is high enough so that the initial state is ionized effectively during the laser pulse but remains about 20% population at the end of the laser pulse. We find that the ionization process of the initial state is very sensitive to the CEP during the laser pulse. The ionization process of the initial state determines the continuum state population and hence influences dramatically the weights of the classical trajectories that contribute to HHG. In such a case we can not predict the cutoff and the structure of the harmonic spectrum only by the number and the kinetic energy of the classical trajectories. The harmonic spectrum exhibits abundant characters for different CEP cases. As a result, we can control the cutoff frequency and the plateau structure of the harmonic spectrum with CEP by controlling the time behaviour of the ionization of the initial state.