Petra and Dirk Wunderlich were educating their four children at home in August 2013 when more than 30 police officers and social workers raided their home and forcefully removed the children.
They were later returned.
The European Court of Human Rights ruled in January this year that the German authorities' actions were not in violation of the Wunderlich family's fundamental rights.
Robert Clarke, director of European advocacy for ADF International and lead counsel for the Wunderlich family said in a statement: "Despite the right of parents to direct the education of their children being protected in international law, the Court ruled that the dawn raid on the family home was neither 'particularly harsh (nor) exceptional.
"We will continue to support the Wunderlich family as they seek affirmation of their rights at the highest level of the European Court of Human Rights."
Germany is one of a minority of countries in Europe that does not allow home schooling for children.
The father of the four children in the case said that it is "upsetting that the European Court of Human Rights did not recognise the injustices we suffered at the hands of the German authorities".
He added: "We are hopeful that the Grand Chamber will see the ways we tried, for many years, to engage with the authorities, and the completely disproportionate action they ultimately took."
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