I saw this sentence in Duolingo. Is this supposed to be dative? If so, why?
 »jemandem glauben« (Dativ): sich auf jemanden vertrauensvoll verlassen
The verb glauben can take both an accusative and dative object. The something you believe is accusative, the person who you believe is dative.
Ich glaube dir[dative] das[accusative] nicht.
The dative form of mein is meinem. Again, Wiktionary is quite a good help.
Thus, it's correct to say:
Er glaubt meinem Kind.
This is a possessive pronoun, dative, "male" grammar-gender.
OP already used "possessive pronoun" as tag, "suggested" dative himself. The only information you added is wrong, because "Kind" is neuter, not masculine. And you didn't say why; which is the actual question.– Em1Jul 12, 2014 at 19:54