  We present results of a search for variable stars in the intermediate-age
open cluster NGC 7044. We found 23 variable stars in the observed field. One
star turned out to be of the delta Sct type with two pulsational modes excited.
From the position in the color-magnitude diagram we conclude that this star is
a member of the cluster. Moreover, we found 13 eclipsing systems, of which five
are W UMa stars, one is a beta Lyr variable, six are beta Per binaries showing
detached configuration, and the last one is another probable beta Per system.
Using the period-luminosity-color relation for W UMa stars we established the
membership of the contact binaries, finding four of them to be very probable
cluster members. We estimated from these four stars an apparent distance
modulus (m-M)_V of NGC 7044 to be 14.2 +/- 0.4 mag, which is smaller than
previous determinations of this parameter. We were able to derive orbital
period for only four beta Per systems. For the remaining ones we observed only
two or three eclipses. Finally, nine stars we found to show irregular light
changes. Most of them are red stars not belonging to the cluster. For the
cluster core we determined a reddening map, which allowed us to construct a
dereddened color-magnitude diagram of NGC 7044 with a narrow main-sequence. By
fitting a theoretical isochrone to this diagram we derived E(V-I_C) = 0.92 mag,
(m-M)_V = 14.45 mag and log(age/yr) = 9.2.
