  We theoretically investigate qualitative features of the field-temperature
($H$-$T$) phase diagram of superconductors with strong attractive interaction
lying in the BCS-BEC crossover regime. Starting with a simple attractive
Hubbard model, we estimate three kinds of characteristic fields, i.e., the
pair-formation field $H^*$, the vortex-liquid-formation field $H_\mathrm{c2}$,
and the vortex-lattice-formation field $H_\mathrm{melt}$. The region between
$H_\mathrm{c2}$ and $H_\mathrm{melt}$, as well as that between $H_\mathrm{c2}$
and $H^*$, is found to be enlarged as the interaction is stronger. In other
words, a strong attractive interaction can stabilize both the vortex-liquid and
preformed-pair regions. We also point out the expected particle-density
dependence of the $H$-$T$ phase diagram.
