In this paper, we performed molecular dynamics simulations to study the fracture characteristics of a graphene nanoribbon encapsulated in a single-walled carbon nanotube (GNR@SWCNT) subjected to a uniaxial tensile loading. The effects of size and temperature on the fracture strength of nanocomposites under different strains were examined. The fracture strength and fracture strain of the nanocomposites increase with decreasing nanotube diameter. The maximum fracture strength and the corresponding fracture strain of GNR@SWCNT with a (10, 10) nanotube at 300 K were 126.3 GPa and 0.36, respectively. However, the fracture strength and fracture strain decrease with increasing temperature. The simulation results are useful in the design of nanodevices composed of carbon nanotubes and graphene nanoribbons.