In 2024, the Euler-Sombor index (EU) was introduced based on the calculation of the circumference of an ellipse, which is defined as \[ EU(G) = \sum_{uv \in E(G)} \sqrt{d(u)^2 + d(v)^2 + d(u)d(v)} \ . \] In this paper, we present the maximum values of the Euler-Sombor index of trees with some given parameters, such as the matching number, the number of pendent vertices and the diameter.