In this paper, the multifractal properties of the ion current time series in the fast-activating vacuolar (FV) channels of L. taproot cells were investigated. These channels are permeable for only monovalent cations and mediate K at very low concentrations of cytosolic Ca and large voltages of either polarity. Using the patch clamp technique, the currents of the FV channels in red beet taproot vacuoles were recorded and analysed by using the multifractal detrended fluctuation analysis (MFDFA) method. The activity of the FV channels depended on the external potential and was sensitive to the auxin. It was also shown that the singularity spectrum of the ion current in the FV channels is non-singular, and the multifractal parameters, i.e., the generalised Hurst exponent and the singularity spectrum, were modified in the presence of IAA. Taking into account the obtained results, it can be suggested that the multifractal properties of fast-activating vacuolar (FV) K channels, indicating the existence of long-term memory, should be taken into account in the molecular mechanism of the auxin-induced growth of plant cells.