  Aging phenomena have been observed in numerous physical systems. Many
statistical quantities depend on the aging time $t_a$ for aging anomalous
diffusion processes. This paper pays more attention to how an external force
field affects the aging L\'{e}vy walk. Based on the Langevin picture of
L\'{e}vy walk and generalized Green-Kubo formula, we investigate the quantities
which include the ensemble- and time-averaged mean-squared displacements in
both weak aging $t_a\ll t$ and strong aging $t_a\gg t$ cases, and compare them
to the quantities in the absence of any force field. Two typical force fields,
constant force $F$ and time-dependent periodic force $F(t)=f_0\sin(\omega t)$,
are considered for comparison. The generalized Einstein relation is also
discussed in the case with constant force. We find that the constant force is
the key of generating the aging phenomena and enhancing the diffusion behavior
of aging L\'{e}vy walk, while the time-dependent periodic force is not. The
different effects of the two kinds of forces on the aging phenomena of L\'{e}vy
walk are verified by both theoretical analyses and numerical simulations.
