“Than me” is grammatical. Many people are taught that only than I is correct, but that is too simple. In modern English, than can function as a preposition as well as a conjunction, so an object pronoun after it is normal.
That is why sentences like She is taller than me and He knows more than us are standard, especially in everyday speech and writing.
You may also see a more expanded form, such as She is taller than I am. That version is also correct. It treats than as introducing a clause, with the verb understood or stated.
- Everyday style: She is taller than me.
- More formal or expanded style: She is taller than I am.
- Another common example: They arrived earlier than us.
- Expanded version: They arrived earlier than we did.
The best choice often depends on style, not correctness. If you want a natural conversational tone, than me is fine. If you want a more formal or fully stated structure, than I am may feel better. Both are part of standard English.