The coexistence of both electric and magnetic orders in some metal-organic frameworks (MOFs) has yielded a new class of multiferroics beyond inorganic materials. However, the coupling between two orders in multiferroic MOFs has not been convincingly verified yet. Here we present clear experimental evidences of cross coupling between electric and magnetic orders in a multiferroic MOF [(CH3)2NH2]Fe(HCOO)3 with a perovskite structure. The dielelectric constant exhibit a hump just at the magnetic ordering temperature TN. Moreover, both the direct (magnetic field control of dielectric properties) and converse (electric field control of magnetization) magnetoelectric effects have been observed in the multiferroic state. This work opens up new insights on the origin of ferroelectricity in MOFs and highlights their promise as magnetoelectric multiferroics.