John Allen Rubio, 29, of Brownsville, Texas, was found guilty in 2003 of killing the three children - all under the age of four - but an appeals court overturned the conviction in 2007. He was again sentenced to death on Thursday for the beheading of the three - including his own daughter, the Herald Sun reported.
Rubio told the court that after killing the children, he insisted that Angela Camacho - the children's mother - have sex with him, saying that it would be their last chance.
Police found the decapitated bodies of Julissa Quesada, three, John E Rubio, one, and two-month-old Mary Jane Rubio March 11, 2003. The youngest child was Rubio's biological daughter.
They were discovered in the apartment in Brownsville where the family lived. Camacho had pleaded guilty in 2005. She is currently serving three life sentences.
The court sentenced Rubio to death by lethal injection, but his attorney said he will appeal the conviction.
Rubio, however, pleaded not guilty to insanity.
Published 30 July 2010, 09:18 IST