In this paper we consider one dimensional general mean-field backward stochastic differential equations (BSDEs), i.e., the generator of our mean-field BSDEs depends not only on the solution but also on the law of the solution. We first give a totally new comparison theorem for such type of BSDEs under Lipschitz condition. Furthermore, we study the existence of the solution of such mean-field BSDEs when the coefficients are only continuous and with a linear growth.