I am an asylee with approved asylum case, applied for Refugee Travel document before I left the States.

Without having your refugee travel document in hand, you might certainly have a difficult time at the port of entry. Assuming that you are even able to make it to the port of entry in that the air carrier (if flying in) has allowed you to board, the immigration inspector would certainly place you in secondary inspection and you would likely be stuck there for quite some time while Customs and Border Protection decides what to do with you. Ultimately they may allow you back in, but it may be quite an ordeal for you. I note a 1999 memorandum from legacy INS that a person in your situation is inadmissible and subject to removal proceedings and may not resume status in the U. S. unless he or she applies for and is granted a refugee travel document at a U. S. consulate or port of entry, or is granted parole back into the country. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (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.