We have performed dielectric measurements and neutron diffraction experiments on the delafossite AgFeO2. A ferroelectric polarization P is approximately equal to 300 μC/m2 was observed in a powder sample, below 9 K. The neutron diffraction experiment demonstrated successive magnetostructural phase transitions at T(N1)=15 K and T(N2)=9 K. The magnetic structure for 9 K≤T≤15 K is a spin-density wave with a temperature dependent incommensurate modulation k=(-1, q, 1/2), q is approximately equal to 0.384. Below 9 K, the magnetic structure turns into elliptical cycloid with the incommensurate propagation vector k=(-1/2,q,1/2), q is approximately equal to 0.2026 Based on the deduced magnetic point-group symmetry m1' of the low-temperature polar phase, we conclude that the ferroelectric polarization in AgFeO2 is perpendicular to the monoclinic b axis and is driven by the inverse Dzyaloshinskii-Moriya effect with two orthogonal components p1 is proportional to r(ij)×(S(i)×S(j)) and p2 is proportional to S(i)×S(j).