A novel electrochemical glucose sensor was developed, based on a multiwall carbon nanotubes (MWCNTs)-copper-1,3,5-benzenetricarboxylic acid (CuBTC)-epoxy composite electrode, named MWCNT-CuBTC. The electrode nanocomposite was prepared by a two-roll mill procedure and characterized morphostructurally by scanning electron microscopy (SEM). The CuBTC formed defined crystals with a wide size distribution, which were well dispersed and embedded in the MWCNTs. Its electrical conductivity was determined by four-point probe contact (DC) conductivity measurements. The electroactive surface area, determined using cyclic voltammetry (CV), was found to be 6.9 times higher than the geometrical one. The results of the electrochemical measurements using CV, linear sweep voltammetry (LSV), differential pulse voltammetry (DPV), chronoamperometry (CA) and multiple pulse amperometry (MPA) showed that the MWCNT-CuBTC composite electrode displayed high electrocatalytic activity toward the oxidation of glucose and, as a consequence, very high sensitivity. The best sensitivity of 14,949 µAmM−1cm−1 was reached using MPA at the potential value of 0.6 V/SCE, which was much higher in comparison with other copper-based electrodes reported in the literature. The good analytical performance, low cost and simple preparation method make this novel electrode material promising for the development of an effective glucose sensor.