The effect of carbon nanotubes (CNTs) on the capillary extrusion behavior of low-density polyethylene (PE) was investigated. From the linear viscoelasticity and the morphology observation, it was found that the CNTs were well dispersed throughout the PE matrix and our system belonged to the semi-dilute regime. The strain hardening, which quantifies the extension of the PE chain, decreased by presence of CNTs in the uniaxial elongational deformation. In contrast, the normal stress difference was almost unaffected by CNTs in the shear deformation. The capillary extrusion behavior revealed that swell ratio decreased with increasing the CNT content although melt fracture was promoted. We summarize that the suppression of swell and promotion of melt fracture are attributable to the orientation of CNTs.