Can private university graduates apply for special post teachers?

Education education answers for you:

Yes, as long as they are graduates of full-time ordinary colleges and universities with bachelor degree or above, or graduates of full-time ordinary colleges and universities who have obtained the qualification of teachers in the past three years, they have good political quality, support the party's principles and policies, love education, have a strong sense of professionalism and responsibility, have good conduct, abide by the law, perform well during school or work (unemployment), and have not received any disciplinary action.

There is only one exclusion condition: in-service special post teachers or national in-service public officials are not allowed to take the special post teacher recruitment examination.

So, if you meet the above conditions, you can apply. The specific conditions need to pay attention to the recruitment announcement issued by the area where you want to apply.