Backward Raman amplification (BRA) in plasma, as a promising amplification technique, has been theoretically predicted to achieve multi-petawatt peak powers using millimeter-scale plasmas. However, under stronger intensity or high plasma densities, self-focusing, filamentation and degradation of pulse focusability often arise. To address these, we propose a scheme that suppresses laser pulse filamentation in high-density plasmas by employing a structured plasma. This approach exploits the balance between self-focusing and diffraction in different layers, thereby preserving the Gaussian profile and focusability of laser pulses. Nonlinear envelope models and particle-in-cell simulations confirm that the structured plasma not only improves energy conversion efficiency but also maintains excellent focusability. In contrast to conventional BRA, our scheme promotes the transition to the high-gain region, offering the merits of high efficiency, high spatial mode quality and great focusability, which may be a key step for the improvement of the competitiveness and practicality of plasma-based amplifiers.