A solid-state drawing and winding process was done to create thin aligned carbon nanotube (CNT) sheets from CNT arrays. However, waviness and poor packing of CNTs in the sheets are two main weaknesses restricting their reinforcing efficiency in composites. This report proposes a simple press-drawing technique to reduce wavy CNTs and to enhance dense packing of CNTs in the sheets. Non-pressed and pressed CNT/epoxy composites were developed using prepreg processing with a vacuum-assisted system. Effects of pressing on the mechanical properties of the aligned CNT sheets and CNT/epoxy composites were examined. Pressing with distributed loads of 147, 221, and 294 N/m showed a substantial increase in the tensile strength and the elastic modulus of the aligned CNT sheets and their composites. The CNT sheets under a press load of 221 N/m exhibited the best mechanical properties found in this study. With a press load of 221 N/m, the pressed CNT sheet and its composite, respectively, enhanced the tensile strength by 139.1 and 141.9%, and the elastic modulus by 489 and 77.6% when compared with non-pressed ones. The pressed CNT/epoxy composites achieved high tensile strength (526.2 MPa) and elastic modulus (100.2 GPa). Results show that press-drawing is an important step to produce superior CNT sheets for development of high-performance CNT composites.