We present the catalog of RR Lyr stars discovered in a 4.5 square degrees area in the central parts of the Large Magellanic Cloud (LMC). Presented sample contains 7612 objects, including 5455 fundamental mode pulsators (RRab), 1655 first-overtone (RRc), 272 second-overtone (RRe) and 230 double-mode RR Lyr stars (RRd). Additionally we attach alist of several dozen other short-period pulsating variables. The catalog data include astrometry, periods, BVI photometry, amplitudes, and parameters of the Fourier decomposition of the I-band light curve of each object. We provide a list of six LMC star clusters which contain RR Lyr stars. The richest cluster, NGC 1835, hosts 84 RR Lyr variables. The period distribution of these stars suggests that NGC1835 shares features of Oosterhoff type I and type II groups. All presented data, including individual BVI observations and finding charts are available from the OGLE Internet archive at ftp://sirius.astrouw.edu.pl/ogle/ogle2/var_stars/lmc/rrlyr