Cameron Brown, 47, allegedly took Lauren to an isolated spot where they could not be seen.
He is then said to have grabbed her and hurled her 120ft into the sea.It is the second time Brown has been on trial for the alleged murder after the jury failed to reach a decision three years ago.
The American was said to have been trying to dodge his £608-a-month child support to Sarah KeyMarer, a British woman who emigrated to the US.
Deputy district attorney Craig Hum told Los Angeles superior court: "This man picked up Lauren, whom he fathered but was never a father to, and threw her off a cliff into the waters."
Brown said the death at Rancho Palos Verdes, near LA, in 2000 was an accident. The trial continues.
This is a sad day in bed rock when a man choose to kill his own child to avoid paying child support. I think that this low life deserves the death penalty. The premeditated act that was committed by this father shows that he not only did not care about himself or his child. Although I do have a problem with the Court system putting children on men who are not a participating member of the child's life. If their is never any contact with the child, why should anyone have to pay child support? If a man says that he does not want the child and the woman decides to keep that child, it should be her responsibility and only hers! Until their is some continuity and equality in making choices in custody and the amount of money paid, their will remain confusion and men representing decision that are very unorthodox. Maybe with more news exposure of how unfair the child support system are, it can help to remedy several problems within the child support system.