To study the effect of cytoskeleton (CSK) with different spreading degrees on substrate and the role of Intermediate filament (IF), a new tensegrity model considering the IF was proposed to simulate CSK of different spreading degrees. First, the vertex coordinates and the centroid positions of the tensegrity of different spreading states were calculated. Then, tensegrity models under displacement loads were established by using the finite element method. Larger spreading degree of CSK resulted in the greater reaction on the substrate under the same deformation regardless of IF. The overall stiffness of CSK was significantly improved when IF was considered. The reaction force of CSK on the substrate was positively correlated with the spreading degree. IF played a key role in CSK.