Nope, 1991. That eight-year technologically upgraded version of WWII in the 1980s was the First Gulf War. 2003 was the Third.
Actually that was called the Iran-Iraq war. Though that war was also called the first Persian gulf war, the Gulf war of 1991 was never called the second gulf war. Second Gulf war is by no doubt the war we now call the Iraq war started in 2003. First the war in 1991 was also called the Iraq war, untill 2003.