In　this　paper,　the　parameter　identification　problem　for　a　general　class　of　time-delay　chaotic　systems　is　considered.　The　objective　of　the　problem　is　to　determine　optimal　values　for　an　unknown　time-delay　and　unknown　system　parameters　such　that　the　dynamic　model　of　the　system　best　fits　given　experimental　data.　We　propose　a　gradient-based　optimization　algorithm　to　solve　this　problem,　where　accurate　values　for　the　partial　derivatives　of　the　error　function　are　obtained　by　solving　a　set　of　auxiliary　time-delay　systems.　Simulation　results　for　two　example　problems　show　that　the　proposed　algorithm　is　robust　and　efficient.