The magnetoelectric coupling effect in materials provides an additional degree of freedom of physical states for information storage and shows great potential in developing a new generation of memory devices. We use an alternative concept of nonvolatile memory based on a type of nonlinear magnetoelectric effects showing a butterfly-shaped hysteresis loop. The state of magnetoelectric coefficient, instead of magnetization, electric polarization, or resistance, is utilized to store information. Because this memory concept depends on the relationship between the charge and magnetic flux, it is actually the fourth fundamental circuit memory element in addition to memristor, memcapacitor, and meminductor, and is defined as memtranstor. Our experiments in memtranstor comprised of the[Pb(Mg1/3Nb2/3)]0.7[PbTiO3]0.3(PMN-PT)/Terfenol-D and Ni/PMN-PT/Ni multiferroic heterostructures clearly demonstrated that the magnetoelectric coefficient can be repeatedly switched not only between positive and negative polarities but also between multilevel states by applying electric fields, confirming the feasibility of this principle. In addition to nonvolatile memory, the nonvolatile logic functions, such as NOR and NAND and synaptic plasticity functions, such as long-term potentiation/depression and spiking-time-dependent plasticity are implemented in a single memtranstor by engineering the applied electric-field pulses. The combined functionalities of memory, logic, and synaptic plasticity enable the memtranstor to serve as a promising candidate for future computing systems beyond von Neumann architecture.