Anisotropic diffusion in the nervous system is most commonly modeled by the apparent diffusion tensor, which is based on normal diffusion theory. However, the departure of the diffusion-induced signal attenuation from the mono-exponential form indicates the existence of anomalous diffusion. The fractional motion (FM) model, which is considered as the appropriate anomalous diffusion theory for biological tissues, has been applied to diffusion MRI. However, the directional sensitivity of the FM model in biological tissues remains elusive. In this study, this issue was addressed via tensor analysis in analogy with the diffusion tensor.