when did jurassic world open?

Started construction in 2001 I believe and opened in 2005.

primal king, you are a life saver

Since the events of the movie are supposed to mainly take place this year, and that it has been stated that it has been 10 years since it opened, it had to be sometime in 2005.

As for construction, I'm guessing that it took at least 2 years for the park to become operational, so Masrani commenced building sometime during 2003 or late 2002.

Simon Masrani used subsidaries Axis Boulder Engineering and Timack Construction to work on the preparation and planning prior to construction on the island. Construction workers were protected from native wildlife by InGen security over the course of the three years from 2002 until completion in 2004. With over $1.2 billion alone spent in concrete and building materials, this project was never underestimated.

source: http://www.masraniglobal.com/about/divisions/jurassicworld/index.html

From what I saw on the website and from what I've heard from others, 2004-2006 range.