A large phase shift of the strongly nonlocal spatial optical soliton (SNSOS) was predicted by Guo et al.[Phys.Rev.E 69,016602 (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 10mW around the critical soliton power,which agrees qualitatively with our theoretical result.