As a Libyan Citizen you can not apply for a visit visa to the US inside Libya. You have to go through the US Embassy in Tunis.
Please visit the link giving below which will provide you with all information where and how to apply for an visa to the US.
http://tripoli.usmission.gov/iv_info.html
An "invitation letter" is not requested. Requested is: proof of employment, salary, school certificates, business licenses or any additional evidence showing your ties to your country of residence. You also should provide a specific address in the United States, and evidence that they have sufficient financial resources to cover their proposed stay in the United States.
This is what many people mean by "invitation letter". Your host has to provide you with a statement that he/she will bear all costs (medical costs/hospital if needed), that you will stay at his/her house and that he/she is able to finance all this. Even your flight back if necessary.
Example of an "invitation letter":
http://216.109.125.130/search/cache?ei=UTF-8&p=invitation+letter+to+the+usa&fr=slv8-fp&u=www.immihelp.com/docs/ltrtoparents.html&w=invitation+letter+letters+usa& d=YpxWi-ljPKRW&icp=1&.intl=us
Take care and good luck
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