We systematically study the influence of laser intensities on the dissociation of H + 2 in strong laser fields by numerically solving the time-dependent Schrödinger equation. In Ti:sapphire infrared (IR) laser fields, H + 2 mainly dissociates along 1sσ g and 2pσ u states. The mixture of these dissociative states results in the laser-intensitydependent electron asymmetric localization. When the dissociation process is dressed by a laser field with a very long wavelength, the potential surfaces 1sσ g and 2pσ u degenerate due to the Stark effect, hence the kinetic energy release is changed. When H + 2 is exposed to a strong ultraviolet (UV) pulse, H + 2 is pumped to several excited states by absorbing a few energetic photons, resulting in the molecular dissociation ending with several kinetic energy peaks. The discrepancy of simulation results from the numerical models with and without Born-Oppenheimer approximation are analyzed.