In　order　to　model　anisotropy　surface　geometry　of　components　in　computer,　the　algorithm　of　anisotropy　fractal　surface　synthesis　was　studied,　where　any　single　or　multi　anisotropy　direction　fractal　surface　with　specified　fractal　parameters　could　be　synthesized　based　on　the　projection　and　rotation　property　of　2D　discrete　Fourier　transform.　And　the　relationship　among　fractal　parameters,　power　spectrum　and　surface　geometry　appearance　was　discussed.　It　is　found　that　anisotropy　fractal　surfaces　can　be　modeled　precisely,　intuitively　and　conveniently　with　respect　to　the　power　spectrum　of　surfaces.　©,　2015,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.