The nonlinear magnetoelectric (ME) effect of voltage harmonic generation in a ring heterostructure, comprising a magnetostrictive layer of an amorphous ferromagnet and a piezoelectric layer of lead zirconate titanate is investigated. The structure was circumferentially magnetized with a permanent field H = 0-40 Oe and excited by a circular alternating magnetic field h = 0-3.6 Oe. At the radial acoustic resonance frequency of the structure of similar to 54.2 kHz, the first voltage harmonic generation efficiency was 2.9 V/(Oe cm), the second was 0.95 V/(Oe(2) cm), and the third was 0.21 V/(Oe(3) cm). The absence of demagnetization effects in the ring structure, in comparison with a planar one, leads to a decrease in the optimal biasing magnetic field as well as to a change in the dependence of the second and third ME voltage harmonics on the magnetic field. The discovered nonlinear effect can be used to create frequency doublers.