Hi ,
I have a Valied L1 Visa till 2014 April. And have applied for a H1 visa in 2013 Quota. So, please help me whether it is ok for me travel India in the month of May and planing to return by end of May.
Absolutely (as long as you are reffering to this year)! You can travel since you have visa till next year.
(I assume you meant FY 2014 H1 quota)
If your H1 is approved, you will be moved to H1 starting Oct 1, 2013 with immediate Change of Status(COS). This is not related to your travel this year before Oct 1, 2013.
If you are planning to travel in May 2014, you can very well travel as long as you go and get stamping done before you return in end of May.
If you leave US while COS is pending, then the same is abandoned. You can return on L-1 and file for separate COS to H-1, or return after getting H-1 visa stamped.