  We study a magnetic field effect on the Non-Fermi Liquid (NFL) which arises
around the quantum critical point (QCP) due to the competition between the
f^2-crystalline-electric-field singlet and the Kondo-Yosida singlet states by
using the numerical renormalization ground method. We show the characteristic
temperature T_F^*, corresponding to a peak of a specific heat, is not affected
by the magnetic field up to H_z^* which is determined by the distance from the
QCP or characteristic energy scales of each singlet states. As a result, in the
vicinity of QCP, there are parameter regions where the NFL is robust against
the magnetic field, at an observable temperature range T > T_F^*, up to H_z^*
which is far larger than T_F^* and less than min(T_{K2}, $Delta).
