Dark matter is now known to be the vital ingredient for the growth of structure in the Universe, while its nature remains a mystery. Lambda cold dark matter (LCDM) model is remarkably successful at explaining the large-scale structure of the Universe, but other dark matter models have similar properties to the LCDM model on linear scales. On the other hand, the structures on non-linear scales (smaller than ~ 1 Mpc) make a difference in dark matter models. In particular, this difference becomes conspicuous in phase space structures of dark matter halos. In this study, we adopt pseudo phase space density (PPSD) profile derived by Taylor and Navarro (2001), which is defined as dark matter density divided by the cube of velocity dispersions of dark matter. N-body simulations predicted that all LCDM halos are strongly related to the power-law radial behavior of the PPSD profiles of halos, PPSD \propto r^-\alpha with \alpha=-1.875. This power-law behavior is identical to that of Bertschinger’s similarity solution for self-similar infall onto a point mass from an otherwise uniform Einstein-de Sitter Universe. The origin of this behavior is unknown but suggests that it reflects fundamental structural properties of LCDM halos. Driven by these motivations, we present the preliminary results of PPSD of dark matter halos in the Galactic dwarf spheroidal galaxies. Moreover, comparing with PPSD calculated from high-resolution dark matter simulations, we discuss whether the LCDM model can reproduce dark matter structures on non-linear scales or not.