We propose a novel definition of orientation distribution function (ODF), which also represents diffusion coefficients for non-Gaussian situations, thus ODF has physical meaning. Then an expression is derived to calculate ODF values through diffusion-weighted signals. Next a new HARDI (high angular resolution diffusion imaging) method called “g-OPDT” (grids orientation probability density transform) is designed for practical use. Numerical simulations are performed to verify its accuracy. ISMRM-2015-Tracto-challenge data are used to quantitatively compare g-OPDT with other methods. Results show that g-OPDT has superior performance on most indicators. In-vivo experiments are conducted to show that its glyph representations have less redundant lobes.