Spin-orbit torque (SOT) based on the spin-orbit coupling (SOC) effect has gained increasing attention in magnetic information storage, logical operation and neuron simulation devices because it can effectively manipulate magnetization switching, chiral magnetic domain wall, and magnetic skyrmion motions. Further improvement of the SOT efficiency and reduction of the driving current density are crucial scientific problems to be solved for high-density and low-power applications of SOT-based spintronic devices. The heavy rare-earth metal dysprosium (Dy) possesses a relatively strong SOC due to the partially filled f orbital electrons (4f¹⁰), which is expected to generate spin Hall torques. In this paper, the impact of Dy thicknesses on the SOT efficiency and SOT-driven magnetic reversal was explored in the Dy/Pt/[Co/Pt]₃ magnetic multilayers, where the rare-earth Dy and [Co/Pt]₃ were used as the spin-source layer and the perpendicularly magnetized ferromagnetic layer, respectively. A series of Dy/Pt/[Co/Pt]₃ heterostructures with various Dy layer thicknesses (t_Dy) of 1, 3, 5 and 7 nm were fabricated by ultrahigh-vacuum magnetron sputtering. The perpendicular magnetic anisotropy, SOT efficiency, spin Hall angle and current-induced magnetization switching were characterized using the magnetic property and electrical transport measurements. The results showed that the switching field and magnetic anisotropic field decreased with an increase in t_Dy, revealing that the magnetic parameters can be regulated by the bottom Dy layer due to their structural sensitivity. However, both damping-like SOT efficiency and effective spin Hall angle (θ_SH^eff) gradually increased with increasing t_Dy, indicating that the rare-earth Dy can provide additional spin current to enhance the SOT efficiency apart from the contribution of Pt/[Co/Pt]₃. Particularly, the maximum θ_SH^eff of 0.379±0.008 was achieved when t_Dy was 7 nm. According to the fitting analysis of the drift-diffusion model, the intrinsic spin Hall angle and spin diffusion length of the rare-earth Dy were extracted to be 0.260±0.039 and 2.234±0.383 nm, respectively, suggesting that Dy can be used as an ideal spin-source material. In addition, the critical switching current density (J_c) gradually decreased with the increase in t_Dy, and J_c reached a minimum value of approximately 5.3×10⁶ A/cm² at t_Dy=7 nm, which is primarily attributed to the increase of the damping-like SOT and slight decrease of the switching field. These results experimentally demonstrate a strong spin Hall effect of the rare-earth Dy, and provide a feasible route for designing SOT-based spintronic devices with low-power dissipation.