In this work,we report the giant electric-field (E-field) induced magnetic anisotropy and magnetization switching in CoNi/Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 (PMN-PT) magnetoelectric heterostructures. For CoNi/PMN-30%PT, the E-field induced anisotropy shows a volatile behavior; whereas for CoNi/PMN-32%PT, a large and nonvolatile E-field induced anisotropy field up to 54kA/m is observed. These behaviors can be understood by measuring the strain vs E-field curves of two kinds of substrates. On the basis of the E-field induced nonvolatile magnetic switching, two stable magnetization states defined by applying E-field pulses were demonstrated in CoNi/PMN-32%PT heterostructure, which paves a new way for voltage-write magnetic random memory devices.Index Terms-ME effect, strain, volatile, nonvolatile