In this work we have investigated the suitability of composite electrodes consisting of cup-stacked and bamboo-like carbon nanotubes (CNT) synthesized directly onto a carbon felt for both lithium storage and double-layer capacitance applications. The CNT/felt composite electrode was prepared using catalytic chemical vapor decomposition on the carbon felt. The microstructure of the electrodes was characterized by scanning electron microscopy. Electrochemical characterization of the CNT/felt, either submitted or not to acid treatment for extraction of the catalytic particles used during the CNT growth, was carried out using 1molL−1 LiPF6 in mixtures of ethylene carbonate, dimethyl carbonate, diethyl carbonate, and propylene carbonate. The carbon nanotubes loading and the type of CNT, whether open or closed, on the felt were the most significant factors regarding the electrochemical properties of the composite. With respect to the application of the composite to lithium storage, an anomalous behavior in the reversible specific capacity as a function of the current was detected. The capacity was found to be large at higher current values. The best reversible specific capacity was found for the open-CNT/felt (275mAhg−1 at 0.16Ag−1, and 200mAhg−1 at 0.82Ag−1), on an area of 0.634mm2. The double-layer capacitance of the CNT decreased with increasing current. In the case of the open-CNT with a CNT loading of 13.93mg, the composite provided 40.3μFcm2 or about 12Fg−1 at 10mA of polarization current using 1molL−1 LiPF6 in mixtures of ethylene carbonate and dimethyl carbonate. For the closed-CNT with a CNT loading of 9.3mg, the double-layer capacitance was 30Fg−1 at 20mA in 1M H2SO4.