Low-dimensional multiferroic systems with magnetoelectric coupling have attracted considerable attention due to their important applications in high-density low-power storage. Based on the first-principles calculations, we demonstrated that the recently proposed one-dimensional (1D) ferroelectric materials NbOCl3 and NbOBr3 have good stabilities, and found that they can be easily separated from the bulk phase. Due to the flat band near the Fermi level, the itinerant ferromagnetism can be induced over a wide range of electron-doping concentrations, and it leads to the coexistence of ferroelectricity and ferromagnetism in 1D NbOX3 (X = Cl, Br) and finite-length nanochains. More interestingly, there is strong magnetoelectric coupling on finite-length nanochains, which is caused by the spontaneous electrical polarization and redistribution of magnetic carriers. In addition, magnetism also can be introduced by oxygen vacancies. We also analyzed the effects of doping concentration, strain, and length on ferroelectric polarization and magnetism. Our findings provide a way to design and search low-dimensional multiferroics.