Gauge/gravity duality has shed light on physics research. It reveals that conformal field theory on the boundary is equivalent to the bulk of anti-de Sitter space-time, which brings us great convenience for studying the conformal field on the boundary. Recently, Susskind et al. proposed a conjecture for complexity/action duality, which states that the quantum computational complexity of the boundary state of a black hole is equivalent to the action in a Wheeler-DeWitt patch. The complexity represents the difficulty of performing quantum computing, which means that black holes may be linked to quantum computing. This provides us with deeper insights on black holes. Based on this conjecture and taking the contribution of null joints into consideration, we improve the original method of Susskind et al., and recalculate the action growth rate of the Wheeler-DeWitt patch of Kerr-AdS black holes more accurately. Finally, we get the complexity of the state on the boundary of Kerr-AdS black hole space-time.