We designed and tested a manufacturing process that resulted in the formation of composites with maximized electrical conductivity and optimized electromagnetic interference (EMI) shielding effectiveness (SE) properties. Single-walled carbon nanotube (SWCNT) paper, which is a microscopic aggregate of van der Waals force interaction, was impregnated with semi-cured epoxy to make SWCNT prepregs. These prepregs were completely cured into SWCNT/epoxy composites. Fabricating and curing processes were executed under proper temperature cycle depending on the time. We inspected SWCNT paper and the interfacial state between the SWCNTs and epoxy in the composite with a field emission-scanning electron microscopy and calculated the SWCNT weight fraction through thermogravimetric analysis measurements. Using these observations, electrical conductivity and EMI SE were investigated according to thickness which could be controlled by the suggested manufacturing process as 1-, 5- and 10-layer composites. Finally, we determined ideal composite thickness and the associated number of prepreg layers using skin depth theory.