  We compute the Hausdorff dimension of the image X(E) of a non random Borel
set E $\subset$ [0, 1], where X is a L\'evy multistable process in R. This
extends the case where X is a classical stable L\'evy process by letting the
stability exponent $\alpha$ be a smooth function, which leads to
non-homogeneous processes because their increments are not stationary and not
necessarily independent. Contrary to the situation where the stability
parameter is a constant, the dimension depends on the version of the
multistable L\'evy motion when the process has an infinite first moment.
