Based on the nonlocal nonlinear Schrdinger equation, which is the evolution equation of propagation of spatial soliton in the nonlocal media, the pulsating propagation of spatial solitons in one-dimensional strongly nonlocal optical lattice are researched numerically by the split-step Fourier method. The pulsating propagation period of spatial soliton is analyzed for different parameters of propagation, such as the initial energy of the beam, the nonlocality degree, the modulation degree of lattice, the period of the transverse modulation and the asymptotic rate of the longitudinal modulation of linear refractive index. And the inherent physical mechanisms of pulsating propagation of spatial soliton are discussed for the different parameters of lattice structure. Furthermore, the controllable switching behavior of spatial optical soliton has been achieved in the strongly nonlocal optical lattice with longitudinal modulation of linear refractive index.