For a simple finite graph G, general sum-connectivity index is defined for any real number α as χα(G) = ∑uv∈E(G) [dG(u) + dG(v)] α, which generalises both the first Zagreb index and the ordinary sum-connectivity index. In this paper, we present some new bounds for the general sum-connectivity index. We also present relation between general sum-connectivity index and general Randić index.