In this paper, we consider a class of nonlinear higher-order wave equation with variable exponents 𝑢𝑡𝑡+(−Δ)𝑚𝑢+|𝑢𝑡|𝑝(𝑥)−2𝑢𝑡=|𝑢|𝑞(𝑥)−2𝑢 in a bounded domain 𝛺⊂𝑅𝑛. We prove a finite time blow up result for the solutions with negative initial energy. This improves earlier results in the literature [18].