Due　to　the　finite　size　of　the　hologram　aperture　in　digital　holography,　high　frequency　intensity　and　phase　fluctuations　along　the　edges　of　the　images,　which　reduce　the　precision　of　phase　measurement.　In　this　paper,　the　apodization　filters　are　applied　to　improve　the　phase　measurement　in　the　digital　holography.　Firstly,　the　experimental　setup　of　the　lensless　Fourier　transform　digital　holography　is　built,　where　the　sample　is　a　standard　phase　grating　with　the　grating　constant　of　300　mu　m　and　the　depth　of　150nm.　Then,　apodization　filters　are　applied　to　phase　measurement　of　the　sample　with　three　kinds　of　the　window　functions:　Tukey　window,　Hanning　window　and　Blackman　window,　respectively.　Finally,　the　results　were　compared　to　the　detection　data　given　by　the　commercial　white-light　interferometer.　It　is　shown　that　aperture　diffraction　effects　can　be　reduced　by　the　digital　apodization,　and　the　phase　measurement　with　the　apodization　is　more　accurate　than　in　the　unapodized　case.　Meanwhile,　the　Blackman　window　function　produces　better　effect　than　the　other　two　window　functions　in　the　measurement　of　the　standard　phase　grating.