  Using elastic and inelastic neutron scattering we show that a cubic spinel,
CdCr$_2$O$_4$, undergoes an elongation along the c-axis ($c > a = b$) at its
spin-Peierls-like phase transition at $T_N$ = 7.8 K. The N\'{e}el phase ($T <
T_N$) has an incommesurate spin structure with a characteristic wave vector
\textbf{Q}$_M$ = (0,$\delta$,1) with $\delta \sim$ 0.09 and with spins lying on
the $ac$-plane. This is in stark contrast to another well-known Cr-based
spinel, ZnCr$_2$O$_4$, that undergoes a c-axis contraction and a commensurate
spin order. The magnetic excitations of the incommensurate N\'{e}el state has a
weak anisotropy gap of 0.6 meV and it consists of at least three bands
extending up to 5 meV.
