We proposed the first threshold GQ signature scheme. The scheme is unforgeable and robust against any adaptive adversary if the base GQ signature scheme is unforgeable under the chosen message attack and computing the discrete logarithm modulo a safe prime is hard. Our scheme achieve optimal resilience, that is, the adversary can corrupt up to a half of the players. As an extension of our work, we proposed a threshold forward-secure signature scheme, which is the threshold version of the most efficient forward-secure signature scheme up to now.