  We obtain the largest catalog of multi-mode $\delta$ Sct stars in the
northern sky to date using the Zwicky Transient Facility (ZTF) Data Release 20
(DR20). The catalog includes 2254 objects, of which 2181 are new to our study.
Among these multi-mode $\delta$ Sct stars, 2142 objects are double-mode
$\delta$ Sct, while 109 objects are triple-mode $\delta$ Sct and 3 are
quadruple-mode $\delta$ Sct. By analyzing the light curves in the $r$ and $g$
bands of the ZTF, we determine the basic parameters of multi-mode $\delta$ Sct
stars, including the periods and amplitudes. Periods are checked by comparison
with the OGLE catalog of double-mode $\delta$ Sct stars. On the Petersen
diagram, multi-mode $\delta$ Sct stars form six sequences. We find that in
Galactic coordinates, the periods of 1O/F double-mode $\delta$ Sct stars at
high latitudes are shorter than those of 1O/F double-mode $\delta$ Sct stars in
the disk, due to metallicity variations. In the future, our catalog can be used
to establish the period--luminosity relation and the period--metallicity
relation of double-mode $\delta$ Sct stars, and to study the Galactic
structure.
