Let (X,Э,μ)d,θ be a space of homogeneous type, i.e. X is a set, Эis a quasi-metric on X with the property that there are constants θ∈ (0，1] and C0 > 0 such that for all x; x1; y∈X, ︱Э(x,y)- Э(x1, y)︱≤C0Э(x,x1) θ[Э(x,y) +Э(x1, y)]1-Э, and μ is a nonnegative Borel regular measure on X such that for some d > 0 and all x ∈ X, μ(｛y∈X: Э(x,y)＜r｝～rd. LetЭ∈ (0,θ], ︱s︱ <ε and max｛d/(d + ε); d/(d + s + ε)｝ < q ≤∞. The author introduces new inhomogeneous Triebel-Lizorkin spaces Fs∞q(X) and establishes their frame characterizations by first establishing a Plancherel-Polya-type inequality related to the norm ‖·‖Fs∞q (X), which completes the theory of function spaces on spaces of homogeneous type. Moreover, the author establishes the connection between the space Fs∞q (X) and the homogeneous Triebel-Lizorkin space Fs∞q (X). In particular, he proves that bmo(X) coincides with F F0∞q(X).