Can my stepfather see me without hijab?

Yes, if your stepfather has consummated his marriage with your mother. In that case he is a permanent mahram, and you don't need hijab in front of him. If they married but never lived together as husband and wife, he is not a mahram, and you keep your hijab on.

What the Quran says

The Quran lists the women a man can never marry. Among them are his stepdaughters, the daughters of his wife, once his marriage with her has been consummated:

وَأُمَّهَـٰتُ نِسَآئِكُمْ وَرَبَـٰٓئِبُكُمُ ٱلَّـٰتِى فِى حُجُورِكُم مِّن نِّسَآئِكُمُ ٱلَّـٰتِى دَخَلْتُم بِهِنَّ "...your wives' mothers, and your step-daughters under your guardianship [born] of your wives unto whom you have gone in..." Quran 4:23

Anyone you can never marry is your mahram, so you can be with him without hijab, travel with him, and be at home with him like with your own father. The phrase "under your guardianship" describes the usual case; the majority of scholars say the rule applies even if you didn't grow up in his house.

The condition: consummation

The verse itself adds that if the marriage wasn't consummated, there is no barrier. So:

Mum and stepdad live together as a married couple: he is your mahram.
Only a contract, no married life yet: he isn't, and you keep hijab.

What if they divorce or your mum dies?

He stays your mahram for life. Mahram status through marriage is permanent, so a divorce or your mother's death doesn't change it, according to the scholars. It works the same way as the father-in-law relationship. See Is my father-in-law a mahram?

What if he isn't Muslim?

Many converts have a non-Muslim stepdad. Mahram status here comes from the marriage, not from his faith, so most scholars say the same rule applies. Some scholars advise a bit more care with a non-Muslim relative, such as dressing modestly around him even without the scarf. For family situations, see Do I need to wear hijab in front of my non-Muslim family?

Safety comes first

Being a mahram means he is someone you can trust like a father. If a stepfather behaves inappropriately, you are not required to uncover or be alone with him, and you should talk to someone you trust or contact local support services.

Key points

A stepfather is a mahram once the marriage to your mother is consummated.
Without consummation, he is not a mahram.
The status stays even after divorce or your mother's death.
Your safety always comes before family rules.

Tip: At home with your stepdad, normal modest home clothes are enough. You don't need to wear your scarf, but you can still choose what you're comfortable in. For the full list, see Who can see me without my hijab?