If you are a US citizen, you can file an immigrant visa ("green card") petition for both of your parents. In general the process takes 6 to 12 months and they would be applying for their green card at the Embassy. Generally they are approved unless there are previous immigration or criminal issues. Contact any US immigration attorney for assistance.
To bring them on a visitor visa they will need to show that they intend to return to their home country, e.g. that they have nonimmigrant intent. This is likely the reason they have been denied. If they have a U.S. citizen child, that child can sponsor them for a U.S. immigrant visa. You might want to talk to an immigration attorney about how to prepare their visitor visa application, although after 4 denials, it will be tough to get an approval.
Due to the nature of this forum, Attorney Maria J. Marty does not have all the information required to provide legal advice. Accordingly, her responses on Avvo are intended as general and not legal advice.
Unfortunately, being denied 4 times means it's unlikey they will get a visa. Without more info it's impossible to tell why it was denied. You also do not indicating if their purpose is of a nonimmigrant (temporary trip) or immigrant intent (to reside here). There is no quick fix. Either you petition for your parent that is their child and wait 5-6 years for that parent to become a citizen and petition for their parents (your grandparents) or you bring them in with humanitarian parole which can be complex, costly and difficult. Speak with an experienced attorney. Do your grandparents have any US citizen children? Like one of your aunts or uncles on that side of the family. A US citizen child could petition for them immediately, just not a U.S. citizen grandchild.
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