We demonstrate all-optical implementation of spin-orbit coupling (SOC) in a two-electron Fermi gas of 173 Yb atoms by coupling two hyperfine ground states with a narrow optical transition. Due to the SU(N ) symmetry of the 1 S0 ground-state manifold which is insensitive to external magnetic fields, an optical AC Stark effect is applied to split the ground spin states, which exhibits a high stability compared with experiments on alkali and lanthanide atoms, and separate out an effective spin-1/2 subspace from other hyperfine levels for the realization of SOC. The dephasing spin dynamics when a momentum-dependent spin-orbit gap being suddenly opened and the asymmetric momentum distribution of the spin-orbit coupled Fermi gas are observed as a hallmark of SOC. The realization of all-optical SOC for ytterbium fermions should offer a new route to a long-lived spin-orbit coupled Fermi gas and greatly expand our capability in studying novel spin-orbit physics with alkaline-earth-like atoms.Ultracold atoms are fascinating for the study of synthetic quantum system which is direct analogy to real electronic material [1]. One of the notable examples is the implementation of synthetic gauge field and spinorbit coupling (SOC) engineered with the atom-light interaction at will [2,3]. In particular, SOC links a particle's spin with its momentum, which is not only essential in novel quantum phenomena, such as spintronic effect [4] and exotic topological states of quantum matter [5,6], but also provides an unprecedented quantum system such as spin-half spin-orbit coupled bosons without analogy in condensed-matter [7]. Various types of SOCs can be generated in ultracold atoms where the relevant parameters are tunable by changing the laser fields [8][9][10] or the magnetic field [11]. So far, the SOCs along the one direction have been created in bosonic alkali [7,[12][13][14][15][16][17][18][19], fermionic alkali atoms [20][21][22][23], and very recently in fermionic lanthanide atoms [24]. Besides the 1D SOC, the two-dimensional synthetic SOCs have been also demonstrated both in the bosonic [25] and fermionic alkali atoms [26].In alkali atoms, two different internal states are coupled through the Raman transition transferring momentum to the atoms [2,3]. However those processes inevitably suffer from heating effect caused by spontaneous emission due to the small fine-structure splitting of the excited level, which could limit the ability to observe interacting many-body phenomena that needs long timescales. Recently to avoid such heating, the specific atomic species with the large ground-state angular momentum such as 161 Dy have been considered [27,28] or the external orbital states, representing pseudo-spins, in optical superlattices have been used to generate SOC [29,30].Here, we expand our capability in exploring a novel SOC physics by implementing SOC with a narrow optical transition in a non-alkali Fermi gas of ytterbium atoms. With a momentum-dependent spin-orbit gap being suddenly opened by switching on the Raman transitio...