  High-energy particle transport in pulsar wind nebulae (PWNe) plays an
essential role in explaining the characteristics revealed in multiwavelength
observations. In this paper, the TeV-gamma-ray-emitting electrons in the Vela X
PWN are approximated to be injected impulsively when the cocoon is formed due
to the interaction between the SNR reverse shock and the PWN. By solving the
diffusion-loss equation analytically, we reproduce the broadband spectral
energy distribution and surface brightness profile simultaneously. The
diffusion coefficient of TeV electrons and positrons, which is well constrained
by the spectral and spatial properties of the TeV nebula, is thus determined to
be $1 \times 10^{26}$\,cm$^{2}$\,s$^{-1}$ for 10\,TeV electrons and positrons.
This coefficient is more than three orders of magnitude lower than that in the
interstellar medium, in agreement with a constraint recently obtained from HAWC
observations of a TeV nebula associated with the Geminga pulsar. These results
suggest that slow diffusion of high-energy particles might be common in PWNe.
