L10-FePt thin film has been considered as a promising material for ultrahigh density perpendicular magnetic recording media. The texture type has a serious impact on the magnetic properties of L10-FePt thin films. In this study, the formation and evolution mechanisms of texture were discussed. The Reuss-Voigt-Hill models were used to determine the anisotropic elastic modulus of L10-FePt thin film with fiber texture. Then the strain energy of thin films under various stress conditions were caclucated. The results revealed the influence of stress condition on the fiber texture evolution. When the L10-FePt thin film was subjected to compressive in-plane strain prior to ordering transformation, the {100} fiber texture will be encouraged. On the contrary, the ordering transformation under tensile in-plane strain was promoted {001} fiber texture formation.