We theoretically investigate BCS-BEC crossover in spinful Haldane model. We find there are two topologically distinct superfluidity phases which are characterized by chern number C=0 and 2, respectively. At half filling, the region of existing of the topological phase is extremely small. However, when the filling factor deviates from half-filling, the regions of topological phase become quite large. With the increasing of interaction, the topologically trival superfluid phase enters topological phase and then reenter topologically trival superfluid phase. This is because with the interaction increasing, the chemical potential displays non-monotonic behaviors. When the spatial inversion is broken, the paring gaps become different between two sublattices of honeycomb lattice. At the same time, a gapless topological superfluid phase appears. However, the region of topological superfluidity phase became smaller. Lastly, we consider Gaussian fluctuations about mean-field phases. Our results show there are two branch collective modes, one is gapless Anderson-Bogoliubov mode, and the other is gapped Leggett mode. Damping of Leggett mode reaches largest values when one approaches topological phase transition points.