Hostage-Taking Act of 1985 - Amends the Federal criminal code to establish criteria for the imposition of the death penalty for hostage taking. Requires the government, when seeking the death penalty, to serve notice upon the defendant a reasonable time before trial or acceptance of a plea of guilty 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 an offense. Provides that no presentence report shall be prepared in such cases. Allows the defendant and the Government to present any information relevant to sentencing, without regard to the rules of evidence, but permits evidence to be excluded where its probative value is substantially outweighed by the danger of unfair prejudice, confusion of issues, or misleading of the jury. Specifies mitigating and aggravating factors which may be established at such hearings. Requires that mitigating factors presented by the defendant be established by a preponderance of the information and aggravating factors presented by the Government beyond a reasonable doubt. Includes as threshold aggravating factors that the defendant: (1) intentionally killed the victim; (2) intentionally inflicted serious bodily injury which resulted in the death of the victim; (3) intentionally participated in an act which he reasonably should have known would create grave risk of death to a person and the victim did die as a direct result of such act; or (4) attempted to kill the President of the United States. Includes among the mitigating factors that the defendant was less than 18 years old at the time of the crime. Conditions imposition of the death penalty on a unanimous finding by the jury that: (1) some aggravating factors exist in addition to a threshold factor; and (2) the aggravating factors sufficiently outweigh any mitigating factor found to exist. Directs the court to impose the death penalty upon a finding that such sentence is justified. 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 death sentence. Establishes procedures for appeal from a death sentence. Requires the court of appeals, upon consideration of 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 the existence of aggravating factors or the absence of mitigating factors. Requires the court to provide a written explanation of its determination. States that the sentence of death shall not be carried out upon a pregnant woman.