Based on first-principles calculations, we predict a one-dimensional (1D) semiconductor with cluster-type structure, namely phosphorus-centered tungsten chloride W₆PCl₁₇. The corresponding single-chain system can be prepared from its bulk counterpart by an exfoliation method and it exhibits good thermal and dynamical stability. 1D single-chain W₆PCl₁₇ is a narrow direct semiconductor with a bandgap of 0.58 eV. The unique electronic structure endows single-chain W₆PCl₁₇ with the p-type transport characteristic, manifested as a large hole mobility of 801.53 cm² V⁻¹ s⁻¹. Remarkably, our calculations show that electron doping can easily induce itinerant ferromagnetism in single-chain W₆PCl₁₇ due to the extremely flat band feature near the Fermi level. Such ferromagnetic phase transition expectedly occurs at an experimentally achievable doping concentration. Importantly, a saturated magnetic moment of 1μ_B per electron is obtained over a large range of doping concentrations (from 0.02 to 5 electrons per formula unit), accompanied by the stable existence of half-metallic characteristics. A detailed analysis of the doping electronic structures indicates that the doping magnetism is mainly contributed by the d orbitals of partial W atoms. Our findings demonstrate that single-chain W₆PCl₁₇ is a typical 1D electronic and spintronic material expected to be synthesized experimentally in the future.