An upgrade, based on Multigap Resistive Plate Chamber (MRPC) technology, of the endcap Time-Of-Flight (ETOF) detector of the Beijing Spectrometer III (BESIII) has been proposed for the replacement of the current scintillator + PMT based ETOF, with the aim of improving the time resolution down to 80 ps sigma. This improvement will enhance the particle identification capability to meet the higher precision requirements of physics. The ETOF system including MRPC modules, Front End Electronics (FEE), CLOCK module, fast control boards and Time to Digital modules (TDIG), has been designed, constructed and parts of the ETOF system have seperately tested. Aiming at examining the quality of entire ETOF system and training the operation of all participated instruments, a cosmic ray test system was built and tested in the laboratory for about three months to guarantee the performance. In this paper the results of the test are presented indicating that the entire ETOF system works well and satisfies the requirements of the upgrade.