Terrorist Death Penalty Act of 1985 - Amends the Federal criminal code to establish criteria for the imposition of the death penalty for any person found guilty of first degree murder in connection with hostage taking.

Requires the Government, for such offense, to serve notice upon the defendant a reasonable time before trial or acceptance of a plea that it intends to seek the death penalty and the aggravating factors upon which it will rely.

Requires a separate sentencing hearing before a jury, or the court upon motion by the defendant, when the defendant is found guilty or pleads guilty to such offense.

Allows the defendant and the Government to present any information relevant to sentencing, without regard to the rules of evidence, but permits information to be excluded where its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading of the jury.

Specifies mitigating factors which the defendant must establish by a preponderance of the information and aggravating factors which the Government must prove beyond a reasonable doubt.

Includes as aggravating factors that the defendant: (1) has previously been convicted of another offense for which a life sentence or death is authorized; or (2) knowingly created a grave risk of death to another person.

Includes among the mitigating factors that the defendant was less than 18 years old at the time of the crime.

Directs the court, or the jury by unanimous vote, to impose the death penalty upon a finding that such sentence is justified based on consideration of both the aggravating and mitigating factors.

Requires the court to instruct the jury not to consider the race, color, national origin, creed, or sex of the defendant in its consideration of the sentence.

Establishes procedures for appeal from a death sentence. Requires the Court of Appeals, upon considering the record and the information and procedures of the sentencing hearing, to affirm the decision if: (1) the sentence was not imposed under influence of passion, prejudice, or arbitrariness; and (2) the information supports the finding of aggravating factors or the absence of mitigating factors. Requires the court to provide a written explanation of its determination.