Abstract: Isochronous fixed field alternating gradient (FFAG) accelerator has received much attention of late years because of advantages like continues beam, and strong focusing, etc. Physical design problems in isochronism FFAG accelerator can be reduced to optimization problems with multiple targets, variables and constraints. Rapid development of multi-objective evolution algorithms (MOEAs) provide the solution to complex optimization problems. Applying MOEAs to isochronous FFAG accelerator optimization makes physical design of isochronous FFAG accelerator efficiently. To validate the effectiveness and practicability, physical design of 70 MeV and 1 GeV isochronous FFAG accelerator was optimized by MOEAs. The performance indexes are able to fulfil the design requirements.