We investigate the co-propagation of a strong pump beam and a weak signal beam in lead glass, and find that the large phase shift of the strongly nonlocal spatial optical soliton （SNSOS） can be realized via cross-phase modulation. The theoretical study suggests a synchronous propagation of the pump SNSOS and the signal SNSOS under the required initial condition. A π-phase shift of the signal SNSOS is experimentally obtained by changing the power of the pump SNSOS by about 13 mW around the soliton critical power, which agrees qualitatively with our theoretical prediction. The ratio of the phase shift rate of the signal SNSOS to that of the pump SNSOS shows a close match to the reciprocal of the ratio between their wavelengths.
