Summary: Let \(G\) be a graph of order \(n\). Denote by \(A\) the adjacency matrix of \(G\) and by \(D=\mathrm{diag}(d_1, \dots, d_n)\) the diagonal matrix of vertex degrees of \(G\). The Laplacian matrix of \(G\) is defined as \(L=D - A\). Let \(\mu_1, \mu_2,\cdots, \mu_{n-1}, \mu_n\) be eigenvalues of \(L\) satisfying \(\mu_1\geq \mu_2\geq \dots \geq \mu_{n-1} \geq \mu_n= 0\). The Laplacian-energy-like invariant is a graph invariant defined as \(\mathrm{LEL}(G) =\sum^{n-1}_{i=1} \sqrt{\mu_i}\). Improved upper bounds for \(\mathrm{LEL}(G)\) are obtained and compared when \(G\) has a tree structure.