Inverse　design　focuses　on　identifying　photonic　structures　to　optimize　the　performance　of　photonic　devices.Conventional　scalar-based　inverse　design　approaches　are　insufficient　to　design　photonic　devices　of　anisotropic　materials　such　as　lithi-um　niobate(LN).To　the　best　of　our　knowledge,this　work　proposes　for　the　first　time　the　inverse　design　method　for　aniso-tropic　materials　to　optimize　the　structure　of　anisotropic-material　based　photonics　devices.Specifically,the　orientation　de-pendent　properties　of　anisotropic　materials　are　included　in　the　adjoint　method,which　provides　a　more　precise　prediction　of　light　propagation　within　such　materials.The　proposed　method　is　used　to　design　ultra-compact　wavelength　division　de-multiplexers　in　the　X-cut　thin-film　lithium　niobate(TFLN)platform.By　benchmarking　the　device　performances　of　our　method　with　those　of　classical　scalar-based　inverse　design,we　demonstrate　that　this　method　properly　addresses　the　crit-ical　issue　of　material　anisotropy　in　the　X-cut　TFLN　platform.This　proposed　method　fills　the　gap　of　inverse　design　of　an-isotropic　materials　based　photonic　devices,which　finds　prominent　applications　in　TFLN　platforms　and　other　anisotropic-material　based　photonic　integration　platforms.