No,
it's still at a constant speed.
It wouldn't matter if you were moving at 100, 1000 or 10000 mph
The speed would still be C
BTW the Speed of Light in Vacuum is 299,792,458 meters per second or about 186,000 miles per
second.
Interestingly, the orbital speed of the Earth is about .01% the speed of light. Add in that The Sun is revolving around the center of the Galaxy, with an orbital velocity of about 200 miles per second. This is about .1% the speed of light. (That's damn fast)
A good link describing your question & validating my answers.
http://www.physlink.com/Education/AskExperts/ae558.cfm