RECTANGLE is a 64-bit block cipher with 80 and 128-bit key length proposed by Zhang et al(Lightweight Cryptography Workshop 2015). Integral attack is one of the typical evaluation tools of block cipher. The designers showed 7-round integral distinguisher. On the other hand, we find 8-round integral distinguisher which has balanced columns by our proposal search method of integral distinguisher. In this paper, we present the first integral attack on reduced-round RECTANGLE. Based on 8-round distinguisher, we can attack 12-round RECTANGLE-128 with computational complexity 2^109.98 with partial sum technique. Also, we can attack 10-round RECTANGLE-80 with computational complexity 270.08.