Using elastic and inelastic neutron scattering we show that a cubic spinel, CdCr2O4, undergoes an elongation along the c axis (c > a = b) at its spin-Peierls-like phase transition at T(N) = 7.8 K. The Néel phase (T < T(N)) has an incommensurate spin structure with a characteristic wave vector Q(M) = (0, delta,1) with delta approximately 0.09 and with spins lying on the ac plane. This is in stark contrast to another well-known Cr-based spinel, ZnCr2O4, that undergoes a c-axis contraction and a commensurate spin order. The magnetic excitation of the incommensurate Néel state has a weak anisotropy gap of 0.6 meV and it consists of at least three bands extending up to 5 meV.