In this paper, an additive white Gaussian noise (AWGN) planar regular relay network (PRRN) is investigated, where the PRRN consists of $n\times m$ relay nodes with $n$ rows and $m$ columns. A finite blocklength (FBL) coding scheme for the AWGN PRRN with receiver-transmitter feedback is proposed, and the corresponding achievable rate is derived. Comparing with the existing achievable rate of the AWGN PRRN, we show that the feedback gain in rate approximately equals log $n$ for fixed $m$ and sufficiently large n, and tends to be a constant for fixed $n$ and sufficiently large $m$. In addition, numerical results show that though increasing $m$ does not help to enhance the rate, it significantly improves the decoding performance of our proposed scheme. Finally, we show that our proposed scheme can be directly applied to the irregular case, where each row of the relay network consists of different number of columns. The study of this paper provides a new way to construct FBL schemes for relay network.