We consider the following functions f n ( x ) = 1 - ln x + ln G n ( x + 1 ) x and g n ( x ) = G n ( x + 1 ) x x , x ∈ ( 0 , ∞ ) , n ∈ ℕ , where G n ( z ) = Γ n ( z ) ( - 1 ) n - 1 and Γ n is the multiple gamma function of order n . In this work, our aim is to establish that f 2 n ( 2 n ) ( x ) and ( ln g 2 n ( x ) ) ( 2 n ) are strictly completely monotonic on the positive half line for any positive integer n . In particular, we show that f 2 ( x ) and g 2 ( x ) are strictly completely monotonic and strictly logarithmically completely monotonic respectively on ( 0 , 3 ] . As application, we obtain new bounds for the Barnes G-function.