Observations of the resolved stars obtained over a period of 11 years in the Local Group dwarf irregular galaxy Pegasus have been used to search for Cepheid variable stars. Images were obtained in 55 epochs in the V band and in 24 epochs in the I band. We have identified 26 Cepheids and have obtained their light curves and periods. On the basis of their position in the period-luminosity (PL) diagram, we have classified them as 18 fundamental modes and eight first overtone Cepheids. Two PL relations for Cepheids have been used to derive the distance, resulting in 1.07 ± 0.05 Mpc. We present the VARFINDER code which finds the variable stars and their predicted periods in a given synthetic color-magnitude diagram computed with IAC-star and we propose the use of the Cepheid population as a constraint of the star formation history of Pegasus.