Composite acrylonitrile–butadiene–styrene (ABS)/carbon nanotubes (CNT) filaments at 1, 2, 4, 6 and 8 wt %, suitable for fused deposition modelling (FDM) were obtained by using a completely solvent-free process based on direct melt compounding and extrusion. The optimal CNT content in the filaments for FDM was found to be 6 wt %; for this composite, a detailed investigation of the thermal, mechanical and electrical properties was performed. Presence of CNT in ABS filaments and 3D-printed parts resulted in a significant enhancement of the tensile modulus and strength, accompanied by a reduction of the elongation at break. As documented by dynamic mechanical thermal analysis, the stiffening effect of CNTs in ABS is particularly pronounced at high temperatures. Besides, the presence of CNT in 3D-printed parts accounts for better creep and thermal dimensional stabilities of 3D-printed parts, accompanied by a reduction of the coefficient of thermal expansion). 3D-printed nanocomposite samples with 6 wt % of CNT exhibited a good electrical conductivity, even if lower than pristine composite filaments.