Ferroelectricity and nanostructure in low-dimensional material are a research hotspot in the condensed matter physics and material science, The low-dimensional material is significant for the application and desig of nano-electronic devices. Based on the density functional theory, the In₂Se₃ monolayer, whose two-dimensional ferroelectricity has already been confirmed in experiment, is selected, and the ferroelectricity in the doped film and its nanoribbons are investigated. It is found that the ferroelectricity and the conductivity can coexist in the doped monolayer, and the electron doping enhances both the in-plane polarization (P_IP) and the out-of-plane polarization (P_OOP), while the P_IP is enhanced and P_OOP is depressed in the case of hole doping. The mechanism of the variation of polarization in the doped film is discussed on the basis of atomic distortions and electronic structures. As the In₂Se₃ nanoribbons are concerned, the one-dimensional ferroelectricity can be found in the In₂Se₃ nanowire, and the local polarization distribution within In₂Se₃ nanoribbons and its band gap are calculated and discussed. Furthermore, the scaling law between the band gap and the width of nanoribbon is obtained by fitting the numerical results. It is expected that our study can broaden the application scope of 2D ferroelectric films and its nanostructures.