  Vela X is a nearby pulsar wind nebula (PWN) powered by a $\sim 10^4$ year old
pulsar. Modeling of the spectral energy distribution of the Vela X PWN has
shown that accelerated electrons have largely escaped from the confinement,
which is likely due to the disruption of the initially confined PWN by the SNR
reverse shock. The escaped electrons propagate to the earth and contribute to
the measured local cosmic-ray (CR) electron spectrum. We find that the escaped
CR electrons from Vela X would hugely exceed the measured flux by HESS at $\sim
10$ TeV if the standard diffusion coefficient for the interstellar medium is
used. We propose that the diffusion may be highly inefficient around Vela X and
find that a spatially-dependent diffusion can lead to CR flux consistent with
the HESS measurement. Using a two-zone model for the diffusion around Vela X,
we find that the diffusion coefficient in the inner region of a few tens of
parsecs should be $<10^{28}{\rm cm^2 s^{-1}}$ for $\sim10$ TeV CR electrons,
which is about two orders of magnitude lower than the standard value for ISM.
Such inefficient diffusion around PWN resembles the case of the Geminga and
Monogem PWNe, suggesting that inefficient diffusion may be common in the
vicinity of PWNe spanning a wide range of ages.
