The torsional instability of a single-walled carbon nanotube containing C60 fullerenes is investigated using molecular dynamics. A newly revealed observation of a reduction of the shear stiffness of the carbon nanotube filled with C60 fullerenes during torsion shows an unusual local buckling nature of the material instead of a global buckling of an unfilled carbon nanotube at a critical torsional angle. Such local buckling largely increases the critical torsional angle for the instability of the material, and hence enhances its stability. Simulations show that the local buckling of the material is a result of the van der Waals interaction between the nanotube and the encapsulated C60 fullerenes.