My credit card company charges me an annual fee of $60.00 a year, and since I didn´t pay it, they also tacked on a late fee.

I haven´t used this card since before the annual fee date, and want to cancel this card-do I have to pay this late fee???

You have to pay the fee. Then, call the credit card company and tell them you want to cancel the card.

Yes this was part of your agreement and you are still responsible for it. Pay the full balance and then they will let you close the credit card.