Let G = (V, E) be a graph. For a function f : V -> {-1, 1}, the weight of f is w(f) = Σ v V f(v). For a vertex v in V, we define f[v] = Σ u N [ v ] f(u). A signed dominating function of G is a function f : V -> {-1, 1} such that f[v] >= 1 for all v V. The signed domination number γ s (G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γ s (G) we call a γ s -function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).