Backward Raman amplification (BRA) in plasma can be used for generating ultra-powerful laser pulses. In this paper, the plasma density effect on backward Raman laser amplification is studied by using particle-in-cell method. It is found that using a low plasma density can lead to the premature Langmuir wave breaking and thus result in a small energy-transfer efficiency. On the other hand, using a high plasma density will enhance the developments of unwanted instabilities, which rapidly disturb the Raman amplification, thus limiting the interaction length and output power. Therefore, an optimal plasma density for BRA is near the threshold of Langmuir wave breaking in order to achieve both high efficiency and large energy flux. The space frequency spectrum analysis shows that the saturated intensity of amplified pulses is limited mainly by the self-phase modulation instability. By using a 1013 W·cm-2 pump pulse, our simulation results show that the initial 1013 W·cm-2 seed pulse can be well be well amplified into a pulse with an energy power of 1017 W·cm-2, a duration of 40 fs, and and an energy conversion efficiency of up to 58%.