Dr. William:

I got my H-1B job position when I was in my home country. After I came to U.S. to work for this employer, I found that I was not paid the wage under the requirements of the H-1B Labor Condition Application. 

Can I leave my current employer and transfer my H-1B to another employer, if I can find a new job?  

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Answer:

As a H-1B employee, you should be paid the wage listed in the H1B Labor Condition Application. You can leave the current H-1B employer. But to qualify for a H1B transfer in this case, you should keep recent pay stubs, it may help you to establish that you have been maintaining valid H-1B status. 

If you have not maintained a valid H-1B status, it may not be possible to obtain an H-1B extension of status within the U.S. However, it does not prevent you from obtaining an H-1B petition approval through a new employer and regaining valid legal H-1B status by traveling abroad, and reentering U.S. on a new I-94 card.