After representing CD Numancia,[2] Kome made his La Liga debut with another Madrid club, Getafe CF, first appearing 15 minutes in a 3–1 home win against Athletic Bilbao.

On 6 February 2005 he scored the game's only goal in a home victory former side Numancia and, after relative playing time, he dropped down to the second level and signed with Ciudad de Murcia.

Kome started the 2006–07 campaign with RCD Mallorca but, after being overlooked, left for Real Valladolid during the January transfer window, on a two-and-a-half-year deal.

[3] However, after being sparingly played and although still under contract, he managed to reach a buyout and moved to CD Tenerife on 21 July 2008, on a Bosman transfer.

[4] On 13 June 2009, Kome scored the game's only goal at Girona FC as his team confirmed their return to the top tier after seven years.