Using a time-dependent density-functional-theory (TDDFT) method that incorporates the exact exchange, we reproduce the measured ionization suppression for vanadium in 1500-nm lasers of 1.4 to 2.8×1013W/cm2. The calculated ionization yields are 0.07 to 0.5 in 100 fs sin2 pulses. For weaker laser intensities a method with more configurations is needed to properly describe the multiphoton, rather than tunneling, ionization of a transition-metal atom. Our calculations show that the isotropic component of the induced potential increases the binding energy of the electron while the dipole component elevates the potential barrier of tunneling ionization. Both effects suppress the tunneling ionization.