The six included the main suspect in the case, Abd al-Rahim al-Nashiri, who is in US custody and being tried in absentia. The five others were in court on Wednesday.
The attack against the US navy destroyer in the southern Yemeni harbour left 17 American sailors dead.
The six were accused of carrying out "the attack against the USS Cole, belonging to the al-Qaida network and undermining Yemen's interests", according to the charge sheet read out during an hour-long hearing.
They were also accused of "being in possession of weapons".
Three officials from the US Justice Department attended part of Wednesday's session at the state security court in Sanaa, held amid tight security.
The court, which opened the trial on 6 June and adjourned for a month, set the next session for 14 July.
Nashiri was arrested in the United Arab Emirates in October 2002 and handed over to Washington.
Right to have Lawyers
The US claimed that Nashiri, born in Saudi Arabia of Yemeni descent, at the time was al-Qaida's chief for naval operations and its operations chief in the Gulf.
He is also suspected of involvement in attacks against the US embassies in Kenya and Tanzania in August 1998 that killed 224 people.
The six were charged for "the attack against the USS Cole, belonging to al-Qaida 'network' and undermining Yemen's interests"
Another incident he is suspected of is involvement in the bombing a French super tanker, Limburg, in October 2002, off south Yemen in which one Bulgarian crew member was killed and 12 others were wounded.
The five others charged are Yemenis, one of whom had his leg in a cast, known as Abu Abd al-Rahman.
Apart from Badawi, 39, they are Fahd al-Qasaa, 30, Maamun Ahmad Ansoa, 30, Ali Muhammad Salih al-Marqab, 30, and Murad al-Saruri, 27.
The defendants did not make any comments, apart from underlining their right to have defence lawyers.
They said they wanted to be defended by Yemeni lawyers Muhammad Naji Allaw and Abd al-Aziz al-Samawi, who are involved in another, similar, trial in Yemen, including the Limburg attack.
A representative for the prosecution said the five "confessed they had been in Afghanistan, where they underwent training in al-Qaida camps, and that they are affiliated to the network".
The representative, Said al-Aql, said the people who rammed an explosives-laden boat into the USS Cole allegedly were Ibrahim al-Thur and Hassan al-Khamiri who had apparently also been in Afghanistan.
Aql accused Nashiri of starting to plot the bombing in 1997. According to him the boat used in the bombing was allegedly bought in Jizan in southern Saudi Arabia and then sent to Yemen.
Abd al-Rahim al-Nashiri is being
tried in absentia
Yemeni officials said, the trial of the Cole suspects had been repeatedly delayed because the US was insisting it be preceded by the arrest of all suspects in the case.
Yemen has at Washington's behest cracked down on suspected al-Qaida members since the 11 September 2001 incidents.