The torsion of a penny-shaped crack in a functionally graded strip is considered. Hankel transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Investigated are the effects of material property parameters and geometry criterion on the stress intensity factor. Numerical results show that increasing the gradient of shear modulus can suppress crack initiation and growth, and that the stress intensity factor varies little with the increasing of the strip's highness.