Nonradial oscillation modes of a neutron star carry valuable information about its internal structure and nuclear physics. For example, astrophysical compact objects may possess a crystallized quark core that can be probed through interfacial oscillation modes excited between the solid quark core and fluid hadronic envelope. The elasticity of the crystallized quark core can make the pressure inside the star anisotropic. In this talk, I will first present the new formulation we developed to calculate nonradial oscillations of anisotropic neutron stars in full general relativity. I will then report a new finding that certain oscillation modes of anisotropic neutron stars can become unstable, which does not happen for the isotropic case. This may allow us to theoretically constrain the amount of anisotropy inside neutron stars.