The　pre-magnification　digital　holography　with　a　microscopic　objective　(MO)　has　become　an　important　mean　for　imaging　and　measuring　of　microscopic　objects.　Based　on　Fresnel　diffraction　theory,　the　point　spread　function　of　digital　off-axis　Fresnel　holographic　system　with　pre-magnification　is　firstly　deduced　in　detail.　The　lateral　resolution　of　this　imaging　system　is　then　analyzed.　The　amplitude　distributions　of　the　point　spread　functions　of　the　MO,　the　holographic　CCD　and　the　whole　imaging　system　are　simulated　respectively.　Then,　the　matching　requirements　between　MO　and　the　holographic　CCD　are　discussed.　Some　ambiguities　about　the　resolution　limitation　in　existing　literatures　are　clarified.　The　results　show　that　only　when　the　image　resolution　of　the　holographic　CCD　is　not　below　the　imaging　resolution　of　the　MO,　the　resolution　of　overall　system　is　dependent　on　the　numerical　aperture　of　the　MO.　Otherwise,　it　is　dependent　on　the　numerical　aperture　of　the　CCD.　It　is　optimum　to　make　the　imaging　resolution　of　the　MO　approach　its　limitation　and　be　equal　to　or　less　than　the　resolution　of　the　holographic　CCD　a　little.　The　simulation　results　verify　the　validities　of　the　theoretical　analysis.