Electrochemical properties of multiwalled carbon nanotubes (MWNTs) have been carefully investigated by using a Li/MWNT cell; the work is described in this paper. The surprising results from the voltage vs. capacity curves under various charging rates indicated that, at constant voltage in the range from 0 to 2.2 V, the capacity under larger current densities is higher than that under smaller current densities; or in other words, at a given capacity the voltage of the Li/MWNTs cell at larger current densities is lower than at smaller current density. This abnormal behavior has also been found by us recently in other carbonaceous materials. For MWNT materials, the slow diffusion rate of lithium ions and the presence of deep potential wells, which cause the shift of E-o, are proposed to be responsible for the anomalous behavior. (C) 2002 The Electrochemical Society.