This paper investigates a multi-hop decode-and-forward (DF) relay-aided non-orthogonal multiple access (MHDF-R-NOMA) scheme. The model overcomes the problems associated with poor channel quality and disconnection communication with the broadcast station for the users through the path from the intermediate relay nodes to deliver the signal to the users. We assume that we have multiple intermediate relay nodes that constitute the path to transmit the signal to two users who have different channel qualities. Consequently, the closed-form expressions for bit error rate (BER) and outage probability (OP) at all intermediate relay nodes and users are derived. In the analysis, the imperfect channel state information (CSI) and imperfect successive interference cancellation (SIC) are taken into account. Computer simulation are presented to validate theoretical analyzes. The results indicate that the degradation of BER and OP performances for the near user is higher than the far user. We also show the superiority of our model over the single relay scheme. Furthermore, the OP of MH-DF-RNOMA outperforms its counterpart in OMA.