Based on previously reported studies, yttria stabilized zirconia [Y0.15Zr0.85O1.93 (YSZ)] has been used as an epitaxial buffer layer on Si(001) substrates. However, a considerable lattice mismatch exists between the YSZ and Si (15.4 %). This work elucidates the reported relationship between the lattice parameter and composition of neodymia stabilized zirconia [(NdXZr11XO21X/2) (NdSZ)]. According to the relation, the lattice parameter of NdSZ is the same as that of Si at x = 0.75. Therefore, if the epitaxial growth of NdSZ thin film with x = 0.75 is realized on a Si(001) substrate, then zero lattice mismatch can be expected. The deposition of NdSZ thin film on Si(001) substrate was done by dynamic aurora pulsed laser deposition (PLD). Results show that cube-on-cube epitaxial growth (NdSZ(001)[100]//Si(001)[100]) is realized between x = 0.16 and x = 0.52. The best composition of epitaxial NdSZ thin film is regarded as x = 0.47 from the point of crystallinity, orientation and lattice mismatch (11.1 %). When composition x is larger than x = 0.57, the NdSZ thin film orientation becomes (111). Results also show that the lattice parameter of the NdSZ thin film is larger than that of NdSZ bulk. For x = 0.47 thin film, the coexistence of the epitaxial (221) domains is detected in addition to the (001) cube-on-cube domain. The (221) domain is formed due to lattice matching of the oxygen sub-lattice, which has an isosceles triangle shape. We produced cube-on-cube epitaxial NdSZ thin film on Si(001) substrate with a very small lattice mismatch. However, such a small lattice mismatch brings about additional (221) domains that have been reported in the epitaxial growth of CoSi2 thin film on Si(001) substrate. The lattice mismatch between CoSi2 and Si is 11.2 %, which is approximately equal to that between NdSZ (x = 0.47) and Si.