Can I apply for US citizen even we're not together?

Generally, eligibility to apply to become a naturalized U.S. citizen requires a foreign national first to be a Lawful Permanent Resident for five years, but the period is three years for most Permanent Residents who have been living together - actually residing together in marital union to a U.S. citizen spouse during the three years immediately before filing the naturalization application. Note, however, that an application may be filed as early as 90 days before the end of the 5-year or 3-year period. The USCIS considers a legal separation to signify dissolution of the marital union, and it generally considers an informal separation the same way. It would be wise to consult with an immigration attorney about all details relating to naturalization eligibility. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

Your husband has to petition for you and you have to prove that you have a real viable marriage.