With an H-1B, you are bound to work for one employer: the one who petitioned for the H-1B on your behalf. You can do what you’d like with your income, but you cannot work for another employer. So, you could certainly invest in rental property, but you couldn’t quit your job and start a real estate business. That would be a violation of your visa and you could be deported and banned from returning to the United States.
The thing here to keep in mind is that although you would actually own the property, you’re still receiving an income from it (or hopefully at least breaking even). However, you’re not working for a second company. Yet, you must remember that you have a limit on the hours that you can devote to work. You should also never make it even look like you’re working for more than one employer (or business, in this case).
Make sure that you get advice from an immigration attorney about the best ways you can go about investing in rentals and managing those properties. We can help at, a legal marketplace for entrepreneurs. We have a service that you may find beneficial. LawTrades Micro gives you the opportunity to ask an experienced lawyer a specific question for a low flat-rate (usually $25). You’d get an answer to your question within 48 hours. Hope you check us out!