When　GM(1,1)　is　used　in　the　life　prediction　of　mechanical　products,　the　experiment　cost　is　saved　and　the　experimental　period　is　shortened.　The　research　on　the　whitening　differential　equation　of　GM(1,1)　indicates　that　both　the　background　value　and　the　initial　value　of　GM(1,1)　have　important　effect　on　the　prediction　accuracy.　In　this　paper,　a　new　PSO-GM(1,1,　λ,　b)　optimization　model　has　been　proposed　to　improve　the　prediction　accuracy　of　GM(1,1).　Firstly　GM(1,1)　has　been　improved　with　the　difference　scheme　and　made　use　of　the　parameter　λ　to　correct　the　background　value;　secondly　the　parameter　b　has　been　used　to　correct　the　initial　value;　lastly　because　of　the　nonlinear　traits　between　the　parameters　λ,　b　and　the　prediction　errors,　Particle　Swarm　Optimization(PSO)　has　been　used　to　solve　the　best　value　of　λ,　b　according　to　the　criterion　of　minimizing　the　absolute　value　of　mean　relative　error,　then　a　new　PSO-GM(1,1,　λ,　b)　optimization　model　has　been　constructed.　The　correction　deduction　and　PSO　calculation　λ,　b　show　that　the　prediction　accuracy　of　the　PSO-GM　(1,　1,　λ,　b)　is　much　higher　than　that　of　the　GM　(1,　1).　The　two　practical　examples　about　the　life　prediction　of　mechanical　products　show　that　the　optimization　method　of　PSO-GM(1,1,　λ,　b)　is　remarkable.　©2007　IEEE.