To investigate the α-d cluster structure of 6Li, the high-energy (p, 2p) reaction for the least-bound proton in 6Li is analyzed. The reaction is treated as a quasi-free p-p knock-out collision in 6Li followed by the n-α breaking-up of 5He. The plane wave impulse approximation is made in the former process and the final-state interaction theory is applied for the latter one. The ground state of 6Li is described by the totally antisymmetrized α-d cluster model wave function, where the relative wave function between the α and d clusters is assumed to have a correct behavior with an inner oscillation and a long tail, which are consistent with high-energy elastic electron scattering. The theory succeeds in understanding the experimental features of this reaction consistently. It is found that the features of this reaction are entirely due to the α-d cluster structure of 6Li and the unboundness of 5He. In particular, in the angular correlation distribution the filling-up of the dip is due to the s-state component of extra proton in 6Li and the s1/2-wave neutron in 5He, and the ratio of peak-to-valley is determined by the tail of the d-cluster wave function. It is, thus, pointed out that this reaction gives detailed information on the three-body correlation of the extra nucleons and the α core in 6Li.