In 1929, H. Weyl proposed that the massless solution of Dirac equation represents a pair of new type particles, the so-called Weyl fermions [1]. However the existence of them in particle physics remains elusive for more than eight decades. Recently, significant advances in both topological insulators and topological semimetals have provided an alternative way to realize Weyl fermions in condensed matter as an emergent phenomenon: when two non-degenerate bands in the three-dimensional momentum space cross in the vicinity of Fermi energy (called as Weyl nodes), the low energy excitation behaves exactly the same as Weyl fermions. Here, by performing soft x-ray angle-resolved photoemission spectroscopy measurements which mainly probe bulk band structure, we directly observe the long-sought-after Weyl nodes for the first time in TaAs, whose projected locations on the (001) surface match well to the Fermi arcs, providing undisputable experimental evidence of existence of Weyl fermion quasiparticles in TaAs.