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The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable x(t), we've got a new form of asymptotic approximation, completed with error bounds, it is constructed for the Jacobi functions ϕμ(αβ) (t) (α > -1) as μ → + ∞. Besides, an accurate approximation with error bounds is also constructed correspondingly for the zeros tμ,8 of ϕμ(αβ) (t) (α ≥ -0) as μ → + ∞, uniformly with respect to s = 1,2,.... [ABSTRACT FROM AUTHOR]