A report by Mary Hartnoll, the council's director of social work, estimates that the Children (Scotland) Act 1995 will cost Pounds 2 million in the first year with costs rising year by year.
The total cost of legislative measures affecting social workers could be more than Pounds 15 million at a time when the council is predicting cuts of Pounds 40 million next year, the report warns.
Glasgow will send the report's findings to the Convention of Scottish Local Authorities which is compiling a nationwide case for more Government funding of council services.
Mary Beckett, Glasgow's social work convener, said: "The council cannot go on taking on new responsibilities and be held legally accountable for these without the funds to make the new legislation a reality."
The Children (Scotland) Act comes into force next April and confers 22 mandatory duties and 15 discretionary powers on local authorities. Mrs Hartnoll says the council's procedures on children in care, child protection, reports for children's hearings, response to referrals and statistical returns will have to be rewritten.
Local authorities have also had to absorb a major change to the rules on children's hearings since October 1 following a finding against the Government by the European Court. This requires children's panel reporters to pass all papers on which decisions are based to the child's parents. Social workers throughout Scotland are now having to review the nature of the information contained in these reports.