Diffusion anisotropy indices (DAIs) are parameters derived from diffusion tensor imaging (DTI) data which describe the morphological characteristics of diffusion tensor within a specific range. DAIs are the measurements used to quantitatively describe the diffusion direction and strength of the hydrone in vivo, so that DAIs enable one to indirectly probe the internal structure of an imaging subject. The reliability of DAIs is of great importance for the analysis and interpretation of DTI data. Based on the geometric characteristic of the diffusion tensor ellipsoid, we propose a new DAI, the ellipsoidal geometric ratio (EGR), to describe the hydrone diffusion anisotropy property. The analysis results of Monte Carlo simulation and human brain DTI data show that the EGR has better contrast and robustness than fractional anisotropy, the most commonly used DAI, and ellipsoidal area ratio at different noise levels. Furthermore, since EGR makes full use of the ellipsoidal volume information, it is more robust than any other DAIs in the fiber crossing case. EGR may be a superior measure of diffusion anisotropy both in quantifying deep white matter with relatively high anisotropy and pericortical white matter with relatively low anisotropy.