Telford & Wrekin Council said the 2m overspend was caused by "volatility" in the numbers of young people cared for by the council.
"Any volatility in the population can cause problems for a small authority without large internal resources," said John Coughlan, corporate director of social care. He has a children's budget of around 12m.
He said: "Overspend is currently projected at eight to 10 per cent, but we have a management plan in place and will balance the budget by the end of the year.
"Most authorities struggle to manage children's budgets and we are a typical example. There will be no job losses or freezing of posts," he added.
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