Abstract: By using the fixed-point theorem of Guo-Krasnoselskii, we give the existence and multiplicity of positive solution for semi-positone second-order discrete periodic boundary value problem, where λ>0 is the parameter, ［1,T］_z={1,2,…,T}, f:  ［［1,T］_z×［0,∞)→R is continuous and there exists constant  D>0,  such that  f(t,u)≥-D, (t,u)∈［1,T］_z×［0,∞),  a: ［［1,T］_z→(0,∞)  and  0sin²(π/2T).

Key words: periodic boundary value problem, semi-positone problem, positive solution, fixed point theorem