  In this paper, we use the "complexity equals action" (CA) conjecture to
discuss growth rate of the complexity in a charged AdS-Vaidya black hole formed
by collapsing an uncharged spherically symmetric thin shell of null fluid.
Using the approach proposed by Lehner $et\, al.$, we evaluate the action growth
rate and the slope of the complexity of formation. Then, we demonstrate that
the behaviors of them are in agreement with the switchback effect for the light
shock wave case. Moreover, we show that to obtain an expected property of the
complexity, it is also necessary for the CA conjecture to add the particular
counterterm on the null boundaries.
