The Trojan Horse Method (THM) was applied to the 3 He+ 7 Li interaction in order to investigate the quasi-free 7 Li(p, α) 4 He reaction. The three-body experiment was performed at 33 MeV corresponding to a 7 Li-p relative energy ranging from 50 keV to 7 MeV. The extracted 7 Li(p, α) 4 He quasi-free crosssection was compared with the behavior of direct data, as well as with the result of a previous THM investigation on the 7 Li(p, α) 4 He reaction off the neutron in 2 H. A good agreement between data sets shows up throughout the energy range investigated, providing a very important validity test of the pole approximation for the THM.