Parents are being charged between GH¢700 and GH¢500 for hostel facilities in some regions.
He said some of the heads who own private hostels are deliberately turning away students with the excuse that the boarding facilities are full.
Dr Letsa in an interview on Accra FM said "Some heads are sabotaging the Free SHS programme and we know what we are talking about but we are very careful that the government policy succeeds in our region."
His comment comes at the back of parents who are being charged between GH¢700 and GH¢500 for hostel facilities in some regions.
School authorities said the boarding house could only accommodate only few.
The situation compelled parents, especially those who had come from far distances, to send their children to hostel facilities.
"The point we are making is that if there are any genuine concerns about the policy that you think government should address, they should have drawn our attention to it long ago.
Dr Letsa speaking on the development said the heads of the SHS in the Volta Region are working against the programme.
"For example, in one of the schools, we realised that a top official of the school has a private hostel so by telling the students that the hostel was full and by charging money, he is turning the people away, then the people went into those private hostel.
"So people have all kinds of strategies to take advantage of the system and we are treating every issues on its own merit, we are looking at them one by one, we are not going to generalise, the investigations are still on-going but we say this is a government policy and you are an employee of the state; we expect you to comply," he said.
The Free SHS policy was launched in Accra on Tuesday, 12 September by the President with a call on Ghanaians to support the policy and to contribute ideas to make it sustainable.
He said he made the Free SHS pledge "because I know that knowledge and talent are not for the rich and privileged alone, and that free education widens the gates of opportunities to every child, especially those whose talents are arrested because of poverty."