A 2-μm-long Ni ion-chelated DNA molecule (Ni-DNA) was found for the first time to possess both memcapacitor and memristor properties; this Ni-DNA molecule is known as a dual memory circuit element (memelement). As a memelement, the state of impedance on Ni-DNA is proportional to the unit number of Ni ions containing a base pair complex (Ni-bp), which is determined by the previously applied external voltage. Interestingly, the impedances of Ni-DNA change in response to a change in the sweeping frequencies of the external bias. Our simulation results also indicate that changes in the effective resistance and capacitance of Ni-bp may be attributed to changes in the Ni ion redox species in the Ni-bp of a Ni-DNA nanowire. Therefore, the working mechanism of a nanowire-type memcapacitor and memristor is revealed. In summary, the Ni-DNA nanowire is shown to be a multi-dimensional memory device, whose memory state depends on the length of DNA and applied external voltages/frequencies.