Can I get married with my boyfriend while he is in the process to fix papers for his parents?

Whether your boyfriend is single or married has no effect upon his ability to sponsor his parents for green cards. I assume that your boyfriend is a US citizen. He must provide I-864 affidavits of support for his parents ensuring that his parents will be able to live in the US without becoming public charges. Your being married would increase his household size and the amount of support required for his parents. You can be either a plus or minus in this regard. If not working and with no assets, you would increase his financial burden. If working and making a decent salary, you could add your salary and assets to his to assist him in his support affidavits for his parents. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.