We have numerically investigated the impact of non-linear impairments on the performance of 400Gbit/s DP-RZ- QPSK transmission system over 1200km standard single mode fiber (SMF-28) having an average span loss of 16dB and with no in-line optical dispersion compensation in the transmission link. Digital backward propagation (DBP) algorithm based on split-step Fourier method (SSFM) is employed along with the coherent receiver to compensate the fiber transmission impairments i.e. chromatic dispersion (CD) and non-linear (NL) impairments. The system performance is monitored in terms of Q-value (calculated form BER) for various signal input launch powers. We further quantify the impact of inter-channel non-linear impairments such as cross-phase-modulation (XPM) and four-wave-mixing (FWM) on the performance of DBP algorithm by investigating the multiple-channel transmission, i.e. 8x400Gbit/s DP-RZ-QPSK system. The results depict efficient performance of DBP algorithm as compared to the system where only linear dispersion compensation is implemented. This shows the promising impact of digital backward propagation algorithm on the high data-rate transmission systems such as 400Gbit/s per single channel which is expected to be a possible data rate for long-haul optical communication systems after 100Gb Ethernet in near future.