Terbium　scandium　aluminum　garnet　(TSAG)　crystals　have　been　widely　used　in　magneto-optical　systems.　We　investigate　the　complex　refractive　index　of　the　TSAG　crystal　in　the　terahertz　frequency　range　using　terahertz　(THz)　time-domain　spectroscopy　in　the　temperature　range　100-300　K.　It　is　observed　that　the　refractive　index　and　the　absorption　coefficient　increase　with　the　THz　frequency.　The　refractive　index　increases　with　the　temperature.　We　measure　the　temperature　coefficient　of　the　refractive　index　of　the　TSAG　crystal　in　the　frequency　range　0.4-1.4　THz.　Furthermore,　the　loss　tangent,　i.e.,　the　ratio　of　experimental　values　of　the　imaginary　and　real　part　of　the　dielectric　permittivity,　is　found　to　be　almost　independent　of　frequency.　TSAG　is　very　promising　for　applications　in　THz　optoelectronics　because　it　has　a　high　dielectric　constant,　low　loss,　and　low　thermal　coefficient　of　the　dielectric　constant.