There is a utility called PKZIP in mainframe and it can be used to ZIP sequential files, VSAM files, PDS, PDSE members. Sample job is given below.
//STEP01 EXEC PGM=PKZIP
//SYSPRINT DD SYSOUT=*
//RTFILE DD DISP=SHR,DSN= input file to be zipped
//ZIPFIL DD DISP=...zip file name
//SYSIN DD *
The Zipped file will be in ASCII mode. So if you want to transfer the zipped file to your PC, then you should transfer it in "binary" mode.