  We present a stable model for quark stars in Rastall-Rainbow (R-R) gravity.
The structure of this configuration is obtained by utilizing an interacting
quark matter equation of state. The R-R gravity theory is developed as a
combination of two distinct theories, namely, the Rastall theory and the
gravity's rainbow formalism. Depending on the model parameters ($\bar{\lambda},
\eta, \Sigma$), the mass-radius relations are numerically computed for modified
Tolman-Oppenheimer-Volkoff (TOV) equations with proper boundary conditions. The
stability of equilibrium configuration has been checked through the static
stability criterion, adiabatic index and the sound velocity. Our calculations
predict larger maximum masses for quark stars, and the obtained results are
compatible with accepted masses and radii values, including constraints from
GW190814 and GW170817 events in all the studied cases.
