Mel Gibson Demands MORE Daddy Time with Lucia

Mel Gibson wants more quality time with his little girl -- and in order to get it ... he's demanding a change to his child custody agreement with Oksana Grigorieva.

Sources connected to the former couple tell TMZ Mel has filed a request with the court ... for additional overnight visits with 1-year-old Lucia.

Under the current agreement ... Mel gets 3 overnights with Lucia every 2 weeks.

Nothing's decided yet -- a hearing is set for September -- but if the judge grants Mel's request, he and Oksana will be much closer to an even 50-50 split of their time with Lucia.