A large phase shift of the strongly nonlocal spatial optical soliton (SNSOS) was predicted by Guo et al. [Phys. Rev. E69, 016602 (2004)]. We investigate the phase shift of the SNSOS in lead glass. It is found that the phase shift rate along the propagating direction of such a soliton is one order larger than that of the local soliton. The theory agrees quantitatively with the experiment on the dependence of the phase shift on the degree of nonlocality. We realize a π-phase shift by changing the optical power by about 10 mW around the critical soliton power, which agrees qualitatively with our theoretical result.