The Russian singer - who has accused her ex-lover of domestic abuse - is said to have asked a judge to increase the monthly payment from $5,000 to $40,000 to help look after their 10-month-old Lucia.
As well as paying for Lucia, Mel also pays for the luxury Los Angeles home where Oksana lives with her daughter and her 13-year-old son Alexander and sources close to the actor are furious she is demanding more.
One told gossip website TMZ: "Lifestyle is not an issue for a baby. Think she knows the difference between a Ford and a Bentley?"
It is thought Judge Scott Gordon is yet to rule on Oksana's petition.
Last month, it was claimed Mel wanted to pay just $6,000 a month in child support.
Lawyers for the 'Braveheart' actor were said to have told a judge overseeing his bitter custody battle with Oksana that the 54-year-old star spends a staggering $7.2 million a year on himself but he does not want to increase payments for his daughter.
According to reports, Mel's lawyers insist some of Oksana's requests - such as he pays for bodyguards - are unnecessary as Lucia is still just a baby.
In contrast, they argue the money he spends on himself is necessary for his living expenses and doesn't include luxuries such as his private jet.
Mel and Oksana have been locked in a bitter dispute since separating in April.
Since their split, audio tapes have been leaked which apparently feature Mel verbally abusing and threatening Oksana.