In　order　to　improve　the　prediction　accuracy,　firstly　GM(2,1)　has　been　improved　with　the　linear　combination　of　the　forward　and　backward　difference　scheme,　where　the　parameter　λ　has　been　used　to　correct　the　background　value;　secondly　the　parameter　ρ　was　used　for　a　multiple　transformation　on　the　initial　data,　a　new　GM(2,1,　λ,　ρ)　has　been　constructed　in　this　paper.　Because　of　the　nonlinear　traits　between　λ,　ρ　and　the　prediction　errors,　they　are　difficult　to　be　solved,　then　GM(2,1,　λ,　ρ)　based　on　Particle　Swarm　Optimization(PSO-GM　(2,1,　λ,　ρ))　has　been　proposed,　where　λ　and　ρ　have　been　constituted　a　two-dimensional　particle　swarm,　absolute　of　mean　relative　error　has　been　as　fitness　function,　its　minimization　has　been　as　objective　function,　then　the　best　λ,　ρ　have　been　solved.　The　practical　examples　show　that　the　speed　of　convergence　in　PSO-GM　(2,1,　λ,　ρ)　is　rapid,　the　prediction　accuracy　is　much　higher　than　that　of　the　GM(2,1),　and　it　can　meet　practical　need.