  We investigate the dynamical quadrupole structure factor of a spin-1/2
$J_{1}$-$J_{2}$ Heisenberg chain with competing ferromagnetic $J_{1}$ and
antiferromagnetic $J_{2}$ in a magnetic field by exploiting density-matrix
renormalization group techniques. In a field-induced spin nematic regime, we
observe gapless excitations at $q=\pi$ according to quasi-long-range
antiferro-quadrupole correlations. The gapless excitation mode has a quadratic
form at the saturation, while it changes into a linear dispersion as the
magnetization decreases.
