We study numerically the phase diagram for s and d-wave fermionic superfluidity/superconductivity with spin-dependent bandwidth imbalance on a two-dimensional square-lattice. We also investigate the spontaneous space symmetry breaking states at low temperatures by solving the Bogoliubov-de Gennes equations. It is found that, the spatial configuration of the order parameter,both the uni-directional Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) states and the two-dimensional FFLO state may show up in the presence of finite spin-dependent bandwidth imbalance. Moreover, we calculate the spectra of local density of states, and the experimental proposals of observing such FFLO states are therefore suggested. We study numerically the phase diagram for s and d-wave fermionic superfluidity / superconductivity with spin-dependent bandwidth imbalance on a two-dimensional square-lattice. We also investigate the spontaneous space symmetry breaking states at low temperatures by solving the Bogoliubov-de Gennes equation. It is found that, the spatial configuration of the order parameter, both of uni-directional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states and the two-dimensional FFLO state may show up in the presence of finite spin-dependent bandwidth imbalance. Moreover, we calculate the spectra of local density of states, and the experimental proposals of observing such FFLO states are prompted.