Stimulated Raman sidescattering (SRSS), especially 90° sidescattering, can play a dominant role in inhomogeneous plasma. Here, we study the SRSS eigenmode excited in steep-gradient plasma on both numerical and theoretical aspects. Particle-in-cell simulations show that strong SRSS eigenmode are excited even when the plasma scale length at the critical density is as short as one laser wavelength. The studies of the dependence of SRSS on scale length show that there is a minimum scale length to ensure the scattered light strong enough to be observed efficiently. And with the plasma scale lengthening the frequency of scattered light gradually approaches the half of the frequency of incident laser pulse. The linear theory about the growth of SRSS in inhomogeneous plasma shows a good agreement with the simulation, which indicates that the linear theory is also generally right for the case of steep-gradient plasma. When ion motion is considered in the simulations, plasma curvature caused by pondermotive force has a significant effect on the properties of scattered light. Moreover, it is found that short plasma density scale lengths can be identified qualitatively based on SRSS eigenmode in the steep-gradient plasma.