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Abstract The unique electronic properties of topological quantum materials, such as protected surface states and exotic quasiparticles, can provide an out-of-plane spin-polarized current needed for external field-free magnetization switching of magnets with perpendicular magnetic anisotropy. Conventional spin–orbit torque (SOT) materials provide only an in-plane spin-polarized current, and recently explored materials with lower crystal symmetries provide very low out-of-plane spin-polarized current components, which are not suitable for energy-efficient SOT applications. Here, we demonstrate a large out-of-plane damping-like SOT at room temperature using the topological Weyl semimetal candidate TaIrTe4 with a lower crystal symmetry. We performed spin–torque ferromagnetic resonance (STFMR) and second harmonic Hall measurements on devices based on TaIrTe4/Ni80Fe20 heterostructures and observed a large out-of-plane damping-like SOT efficiency. The out-of-plane spin Hall conductivity is estimated to be (4.05 ± 0.23)×104 (ℏ ⁄ 2e) (Ωm)−1, which is an order of magnitude higher than the reported values in other materials.