We present experimental evidence for a type-II noncentrosymmetric Weyl state in TaIrTe4 where it has been recently predicted theoretically. We find direct correspondence between angle-resolved photoemission spectroscopy data and calculated electronic structure both in the bulk and the surface, and clearly observe the exotic surface states which support the quasi-one-dimensional Fermi arcs connecting only four Weyl points. Remarkably, these electronic states are spin polarized in the direction along the arcs, thus highlighting TaIrTe4 as an interesting type-II Weyl semimetal with a promising application potential.