High mechanical properties and light weight structures of composite materials and advances in manufacturing processes have increased the use of composite materials in the aerospace and wind energy industries as a primary load carrying structures in complex shapes. However, use of composite materials in complex geometries such as L-shaped laminates creates weakness at the radius which causes delamination. Carbon nanotubes (CNTs) is preferred as a toughening materials in composite matrices due to their high mechanical properties and aspect ratios. However, effect of CNTs on curved beam strength (CBS) is not investigated in literature comprehensively. The objective of this study is to investigate the effect of CNT on Mode I and Mode II fracture toughness and CBS. L-shaped beams are fabric carbon/epoxy composite laminates manufactured by hand layup technique. Curved beam composite laminates were subjected to four point bending loading according to ASTM D6415/D6415M-06a. Double cantilever beam (DCB) tests and end notch flexure (ENF) tests were conducted to determine mode-I and mode-II fracture toughness, respectively. Preliminary results show that 3% CNT addition to the resin increased the mode-I fracture toughness by %25 and mode-II fracture toughness by %10 compared to base laminates. In contrast, no effect on curved beam strength was found.