Sharon Shoesmith was sacked in December last year following an Ofsted report highlighting failings at the council that led to the death of a child known as Baby P after months of abuse and neglect.
At the time of Shoesmith's dismissal, the council said she would not receive any compensation package or "payment in lieu of notice".
A Haringey Council spokesman confirmed that Shoesmith had appealed against the local authority's decision to sack her.
He added: "We cannot comment on the details of that appeal until after a decision is taken by the appeal panel, which is made up of three different councillors from the original panel."
Michael Gove, Conservative shadow children's secretary, condemned Shoesmith's decision to appeal.
He said: "There should be no reward for failure in either the public or private sector."
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