The main objective of this work is to study the effects of carbon nanotubes (CNT) on the strength and electrical properties of cement mortar. Molecular dynamic simulations (MDS) were carried out for the mechanical and electrical properties of the cementitious composite and the associated mechanisms. To model the atomic structure of the Calcium-Silicate-Hydrates (C-S-H) gel, tobermorite 11Å was chosen. Single-walled carbon nanotubes (SWCNTs) embedded in tobermorite structure were tested numerically. In particular, the effect of the concentration of CNT in cement paste was studied. An innovative experiment of electrical characterization of a cementitious composite of carbon nanotubes has been developed.