I have been working with H-1B visa for more than 2 years in the United States. Now, a multinational company wants to hire me as an executive to open their new office and develop new business in U.S. My question is does my time spending in the U.S. with H-1B visa count toward the L1A visa time limit? Thank you.  

Yes, your time spending in the U.S. with H-1B visa will be count toward the L1A visa time limit. 

For executives and managers in a multinational company working in the United States, the L-1A visa maximum time limit is 7 years. The initial L-1A visa time is 3 years, with 2 additional extension times, up to 2 years for each extension. If you have worked on H-1B visa previously, your time spending on H visa will be count to the L1A visa maximum time limit of 7 years.