We report the results of numerical simulations on pump hysteresis and bistability of a dissipative soliton fiber laser. The fiber laser is made of normal-dispersion fibers and passively mode locked by using the nonlinear polarization rotation technique. The dependence of the final steady state on the initial light field is investigated. Bistability between the single-pulse state and the double-pulse state in the mode-locking regime is demonstrated. Different initial conditions could lead to different attractors, even with the same point in the parameter space.