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.
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