Abstract: In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows d²y/dx²+[λ²q₁(x)+λq₂(x,λ)]y=0, where q₁(x)=(x-μ₁)(x-μ₂)(x-μ₃)f(x),f(x)≠0,μ₁<μ₂<μ₃, and λ is a large parameter,but . By using JL function, the complete expression of the formal uniformly valid asymptotic solutions of the equation near turning point is obtained.