Bismuth bromide (α-Bi4Br4) can demonstrate various exotic topological states, including higher-order topological insulator with hinge states and quantum spin Hall insulator with helical edge states. To date, α-Bi4Br4 nanowires can be obtained by using the exfoliation method from the bulk. However, it is still a great challenge to efficiently prepare α-Bi4Br4 nanowires suitable for potential applications, e.g., saturable absorber in ultrafast pulsed fiber lasers. Here, we report the controllable growth of α-Bi4Br4 thin films consisting of nanowires via molecular beam epitaxy technique. We show that the morphology of the α-Bi4Br4 nanowires depends on the growth temperature and BiBr3 flux. In addition, we also achieve α-Bi4Br4 nanowires on NbSe2 and gold substrates. Furthermore, we performed the saturable absorption property of α-Bi4Br4 thin films with a modulation depth of 21.58% and mode-locking at 1556.4 nm with a pulse width of 375 fs in the pulsed fiber lasers. Those results demonstrate the synthesis of quasi-1D topological material α-Bi4Br4, which is expected to be used for the fundamental research of topological physics and potential applications in optical devices.