The council brought in the mandatory training last year after the Rotherham child sex abuse scandal inquiry found taxi drivers had played a "prominent role" in the abuse.
Eleven drivers who have not yet attended the course could have their licences suspended unless they comply.
The council said feedback was positive.
Conwy council was the first in north Wales to launch the courses, which aims to raise awareness of the issue, give advice on the signs and symptoms to look out for and what to do if they suspect abuse.
A report to councillors said 340 drivers - 97% of those licensed in the county - had now attended.
Members are now looking at options on the action to take against those who do not comply.
They include revoking or suspending their licences, considering licence renewal applications or holding a meeting to hear their representations on why they have not attended.
Licensing officers are also in talks with children's charity Barnardo's over the feasibility of introducing an online course, which has already been done in other parts of the country.
More than 300 taxi drivers in Denbighshire have completed training to help spot the signs of child sexual exploitation.