The man was sentenced to five years in prison by the Eastern High Court in Copenhagen in November last year, but the country's Supreme Court ordered a retrial in September after two prison guards caught one of the lay judges sleeping.
"The day the most important witness was examined, he was sleeping," the man's lawyer, Henrik Stagetorn, told AFP.
The lay judge denied the claim.
The incident took place when the lights had been switched off and the curtains drawn so that the court could view video interrogations of the man's three children.
Cases before a Danish high court that can lead to a prison sentence are decided by three lay judges and three legal judges.
The Danish man had previously been convicted by four votes to two, but was on Tuesday acquitted of raping his 14-year-old daughter by five votes to one.
"There was also some other information. ... Something had happened to the main witness that could weaken her credibility," Stagetorn said.
The case was held "behind locked doors", meaning some information was withheld from the public.
The man was on Tuesday sentenced to 10 months in prison for using violence against two of his other children, but was released after being detained for 28 months.