  We present the electrical resistivity data under application of pressures up
to $\sim$ 26 GPa and down to 50 mK temperatures on YbFe$_2$Zn$_{20}$. We find a
pressure induced magnetic phase transition with an onset at $p_c$=18.2$\pm$0.8
GPa. At ambient pressure, YbFe$_2$Zn$_{20}$ manifests a heavy fermion,
nonmagnetic ground state and the Fermi liquid behavior at low temperatures. As
pressure is increased, the power law exponent in resistivity, $n$, deviates
significantly from Fermi liquid behavior and tends to saturate with $n$ = 1
near $p_c$. A pronounced resistivity maximum, $T_\text{max}$, which scales with
Kondo temperature is observed. $T_\text{max}$ decreases with increasing
pressure and flattened out near $p_c$ indicating the suppression of Kondo
exchange interaction. For $p>p_c$, $T_\text{max}$ shows a sudden upward shift,
most likely becoming associated with crystal electric field scattering.
Application of magnetic field for $p>p_c$ broadens the transition and shifts it
toward the higher temperature, which is a typical behavior of the ferromagnetic
transition. The magnetic transition appears to abruptly develop above $p_c$,
suggesting probable first-order (with changing pressure) nature of the
transition; once stabilized, the ordering temperature does not depend on
pressure up to $\sim$ 26 GPa. Taken as a whole, these data suggest that
YbFe$_2$Zn$_{20}$ has a quantum phase transition at $p_c$ = 18.2 GPa associated
with the avoided quantum criticality in metallic ferromagnets.
