  We apply the transformation of mixing azimuthal and internal coordinate or
mixing time and internal coordinate to the 11D M-theory with a stack of
M2-branes $\bot$ M2-branes, then, through the mechanism of Kaluza-Klein
reduction and a series of the T duality we obtain the corresponding background
of a stack of D1-branes $\bot$ D5-branes which, in the near-horizon limit,
becomes the magnetic or electric Melvin field deformed $AdS_3 \times S^3 \times
T^4$. We find the giant graviton solution in the deformed spacetime and see
that the configuration whose angular momentum is within a finite region could
has a fixed size and become more stable than the point-like graviton, in
contrast to the undeformed giant graviton which only exists when its angular
momentum is a specific value and could have arbitrary size. We discuss in
detail the properties of how the electric/magnetic Melvin field will affect the
size of the giant gravitons. We also adopt an ansatz to find the classical
string solutions which are rotating in the deformed $S^3$ with an angular
momentum in the rotation plane. The spinning string and giant graviton
solutions we obtained show that the external magnetic/electric flux will
increase the solution energy. Therefore, from the AdS/CFT point of view, the
corrections of the anomalous dimensions of operators in the dual field theory
will be positive. Finally, we also see that the spinning string and giant
graviton in the near-horizon spacetime of Melvin field deformed D5-branes
background have the similar properties as those in the deformed $AdS_3 \times
S^3 \times T^4$.
