In this paper, we propose a quantum summation protocol, in which the genuinely maximally entangled six-qubit states found by Borras et al., are employed. Because of the excellent properties of the genuinely maximally entangled six-qubit states, the presented protocol allows three participants to compute the summation of their inputs without the help of a trusted third party and preserve the privacy of their inputs, respectively. The participants do not need any unitary operations. In addition, the proposed protocol utilizes the one-step quantum transmission and therefore is congenitally free from Trojan horse attacks. We have also shown that our protocol is secure against other well-known attacks over lossy and noisy quantum channels.