  In the present work, we consider the non-minimal coupling inflationary model
in the context of the constant-roll idea which is investigated by the
first-order formalism. We attempt to find the hidden symmetries behind the
model by the Lie symmetry method. We supply this aim by using the symmetry
features of the Heun function instead of Killing vector approach. We show that
the hidden symmetries of the non-minimal constant-roll inflation in the cases
of power-law and exponential couplings are characterized as a generalized form
of $sl(2, R)$ and $su(1, 1)$ algebra, respectively.
