As a part of the short-period variability survey (SPVS) at Bohyunsan Optical Astronomy Observa- tory, we obtained time-series BV CCD images in the region of the open cluster NGC 1039 (M34). The observations were performed for 22 nights from July 29, 2008 to September 26, 2010. We also made LOAO observations for 10 days from September 18, 2009 to October 30, 2010 to confirm the small variabilties of δ Scuti-type variable stars. In this paper we presented the observational properties of 28 variable stars found in the region. They are seven δ Scuti-type variable stars, two Doradus-type variable stars, four- teen eclipsing binary stars and five semi-long periodic or slow irregular variables, respectively. Only three variables were listed in the GCVS and the rest are newly discovered ones. We have performed multiple- frequency analysis to determine pulsation frequencies of the δ Scuti-type and ɤ Doradus-type variable stars, using the discrete Fourier transform and linear least-square fitting methods. We also have derived the periods and amplitudes of 12 eclipsing binaries from the phase fitting method, and presented the light curves of all variable stars.