The sum-Balaban index of a connected graph \(G\) is defined as
\[J_e(G) = \frac{m}{\mu+1}\sum_{uv \in E(G)} {(D_u + D_v)}^{-\frac{1}{2}},\]
where \(D_u\) is the sum of distances between vertex \(u\) and all other vertices, \(\mu\) is the cyclomatic number, \(E(G)\) is the edge set, and \(m = |E(G)|\). We establish various upper and lower bounds for the sum-Balaban index, and determine the trees with the largest, second-largest, and third-largest as well as the smallest, second-smallest, and third-smallest sum-Balaban indices among the \(n\)-vertex trees for \(n \geq 6\).