We investigate the short-term dynamical evolution of stellar grand-design spiral arms in barred spiral galaxies using a three-dimensional (3D) $N$-body/hydrodynamic simulation. Similar to previous numerical simulations of unbarred, multiple-arm spirals, we find that grand-design spiral arms in barred galaxies are not stationary, but rather dynamic. This means that the amplitudes, pitch angles, and rotational frequencies of the spiral arms are not constant, but change within a few hundred million years (i.e. the typical rotational period of a galaxy). We also find that the clear grand-design spirals in barred galaxies appear it only when the spirals connect with the ends of the bar. Furthermore, we find that the short-term behaviour of spiral arms in the outer regions ($R>$ 1.5--2 bar radius) can be explained by the swing amplification theory and that the effects of the bar are not negligible in the inner regions ($R

accepted for publication in MNRAS. 11 pages, 10 eps figures