The　different　reconstruction　algorithms　are　investigated　and　the　reconstructed　images　are　presented　in　lensless　Fourier　transform　digital　holography.　The　most　employed　three　algorithms,　all　based　on　the　fast-Fourier-transform,　are:　the　convolution　algorithm,　the　angular　spectrum　algorithm,　and　the　Fresnel　algorithm.　With　the　convolution　algorithm　and　angular　spectrum　algorithm,　there　is　an　optimal　reconstruction　distance　where　the　pass-band　range　of　the　transfer　function　is　the　largest.　Then　the　whole　reconstructed　image　with　the　highest　resolution　can　be　acquired.　When　the　distance　is　different　from　the　optimal　distance,　the　size　of　the　reconstructed　image　may　vary　with　the　distance　and　may　disappear　from　the　field　of　view　in　some　cases.　In　order　to　obtain　the　whole　image,　two　methods　are　proposed.　However,　at　this　time　the　resolution　of　the　reconstructed　image　becomes　lower.　When　the　distance　is　smaller　than　the　optimal　distance,　the　whole　image　can　be　obtained,　but　the　resolution　of　the　image　also　decreases.　The　Fresnel　algorithm　is　performed　by　using　a　single　fast-Fourier-transform.　With　Fresnel　algorithm,　the　same　reconstructed　images　can　be　obtained　with　the　different　reconstruction　distances　and　the　reconstruction　is　better　than　with　the　convolution　algorithm　and　the　angular　spectrum　algorithm.