I worked for a foreign corporation's affiliate company for about one year in my home country as a engineering group's leader, but not directly worked for the foreign corporation. Now, this corporation is willing to apply for a L-1 visa for me.

My questions are -  do I have to work for the foreign corporation directly before to qualify a L-1 visa? and what are the major difference between the L-1A visa and the L-1B visa?

The language of the L-1 visa statute is specific in limiting to only those executives, managers, or special knowledge workers who have previously worked for the firm, corporation or other legal entity, or an affiliate or subsidiary of that entity, and are coming to the United States to work for the same entity, or its affiliate or subsidiary. Therefore, you could qualify for a L-1 visa.

The L-1A visa is for managers and executives. A benefit of being on an L-1A visa is the ability to apply for a Green Card (permanent residence), without going through the process of Labor Certification, after only one year in L-1A status. The L-1B Visa is for key employees, such as accountants, engineers, computer programmers.