Although spinel Li4Ti5O12 is an attractive anode material for lithium-ion batteries (LIBs), it suffers from its poor rate performance. To improve the rate performance, a Li3.9Cu0.1Ti5O12 and carbon nanotubes (CNTs) composite was fabricated through mixing CNTs with Li3.9Cu0.1Ti5O12 particles. X-ray diffraction combined with Rietveld refinement, X-ray photoelectron spectroscopy, field emission scanning electron microscope, transmission electron microscope, nitrogen adsorption–desorption measurement, electrochemical impedance spectroscopy, two-terminal electronic conductivity test and galvanostatic discharge–charge test were employed for the characterizations. The Cu+ substituting negligibly changed the particle size but modified the crystal structure. Consequently, the electronic and Li+ ion conductivities of Li3.9Cu0.1Ti5O12 were respectively increased to 4.0×10−8 S cm−1 and 5.6×10−7 S cm−1, which are at least forty and four times larger than those of the pristine Li4Ti5O12. Through incorporating CNTs, the electrical conduction between the Li3.9Cu0.1Ti5O12 particles was enhanced. As a result of these simultaneous improvements arising from the synergistic effect combining intrinsic improvement by Cu+ substituting and extrinsic enhancement by CNTs compositing, Li3.9Cu0.1Ti5O12/CNTs shows a significantly improved rate performance, which is better than those of Li3.9Cu0.1Ti5O12, Li4Ti5O12/CNTs and Li4Ti5O12. The specific capacity of Li3.9Cu0.1Ti5O12/CNTs at 10C is up to 103 mAh g−1 between 1.0 and 2.5V (vs. Li/Li+), in contrast to those of Li3.9Cu0.1Ti5O12, Li4Ti5O12/CNTs and Li4Ti5O12 to be only 29, 68, 12 mAh g−1 at the same rate. In addition, Li3.9Cu0.1Ti5O12/CNTs exhibits high cyclic stability with capacity retention of 96.3% over 100 cycles. These advanced electrochemical performances may render Li3.9Cu0.1Ti5O12/CNTs a promising candidate for the anodes of high-power LIBs.