Private School Non-Discrimination and Due Process Act of 1979 - States Congressional policy with respect to the elimination of racial discrimination in education and the need for judicial review of Internal Revenue Service denial or revocation of tax-exemptions for private schools which are alleged to operate on a racially discriminatory basis. Amends the Internal Revenue Code to prohibit the Secretary of the Treasury from denying or revoking the tax-exempt status of a private school on the grounds that such school discriminates against students on the basis of race unless a court has adjudicated the issue and rendered a declaratory judgment that the school has discriminated. Requires the Secretary to show by a clear and convincing preponderance of the evidence that a private school has had a practice of deliberate and intentional racial discrimination. Prohibits the Secretary from revoking the tax-exempt status of a private school which has been adjudicated as practicing racial discrimination until the school has exhausted all its appeals. Directs that the district court shall retain its jurisdiction in any case in which a private school has been found to practice discrimination to order a reinstatement of the school's tax exemption if the school has adopted a policy of non-discrimination for a period of not less than a full school year since its revocation became final. Awards attorney's fees to a private school which prevails in a suit initiated to terminate its tax exempt status.