The dynamic process of H2+ in intense ultrashort laser pulses with intensities of 1014 ～ 1015 W/cm2, wavelength of 532nm and duration of 22fs is theoretically investigated by using collinear model and numerically solving the time-dependent Schrodinger equation. The results show that: (1) the dissociation and dissociative ionization compete each other in the case of intensities between 2.5 × 1014 and 4.0 × 1014 W/cm2 ; (2) both the dissociation and the dissociative ionization are much smaller and appear at about 5 cycles (≈9fs) later than the ionization.In addition, we estimate the spectrum of high harmonic generation and find that the well-known cutoff rule is invalid for the ultrashort laser pulse (e.g. the duration ~ 25fs), because the shorter pulse can produce higher order harmonics than the longer one.