Let p c(G) be the critical probability of the site percolation on the Cayley graph of group G. Benjamini and Schramm (Benjamini, I; Schramm, O. Electron. Comm. Probab. 1996, 1, 71–82) conjectured that p c < 1, given the group is infinite and not a finite extension of . The conjecture was proved earlier for groups of polynomial and exponential growth and remains open for groups of intermediate growth. In this note we prove the conjecture for a special class of Grigorchuk groups, which is a special class of groups of intermediate growth. The proof is based on an algebraic construction. No previous knowledge of percolation is assumed.