The dynamic process of H₂⁺ in intense ultrashort laser pulses with intensities of 10¹⁴ ∼ 10¹⁵ W/cm², wavelength of 532 nm and duration of 22 fs is theoretically investigated by using collinear model and numerically solving the time-dependent Schrödinger 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 (≈9 fs) 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 ≤ 25 fs), because the shorter pulse can produce higher order harmonics than the longer one.