To solve the fine-tuning problem in μ-term hybrid inflation, we will realize the supersymmetry scenario with the TeV-scale supersymmetric particles and intermediate-scale gravitino from anomaly mediation, which can be consistent with the WMAP and Planck experiments. Moreover, we for the first time propose the μ-term hybrid inflation in no-scale supergravity. With four scenarios for theshow that the correct scalar spectral index n s can be obtained, while the tensor-to-scalar ratio r is predicted to be tiny, about 10 −10 -10 −8 . Also, the SU (2) R ×U (1) B−L symmetry breaking scale is around 10 14 GeV, and all the supersymmetric particles except gravitino are around the TeV scale, while the gravitino mass is around 10 9 -10 10 GeV. Considering the complete potential terms linear in S, we for the first time show that the tadpole term, which is the key for such kind of inflationary models to be consistent with the observed scalar spectral index, vanishes after inflation. Thus, to obtain the μ term, we need to generate the supersymmetry breaking soft term A S κ κ S due to A S κ = 0 in no-scale supergravity, where and are vector-like Higgs fields at high energy. We show that the proper A S κ κ S term can be obtained in the M-theory inspired no-scale supergravity. We also point out that A S κ around 700 GeV can be generated via the renormalization group equation running from string scale. We briefly comment on the supersymmetry phenomenological consequences as well.It is well known that our Universe may experience an accelerated expansion, i.e., inflation [1][2][3][4], at a very early stage of evolution, as suggested by the observed temperature fluctuations in the cosmic microwave background radiation (CMB). From the particle physics point of view, supersyma e-mail: wulina@std.uestc.edu.cn b e-mail: hushan@itp.ac.cn c e-mail: tli@itp.ac.cn metry is the most promising extension for the Standard Model (SM). In particular, the scalar masses can be stabilized, and the superpotential is non-renormalized. Because gravity is also very important in the early Universe, it seems to us that supergravity theory is a natural framework for the inflationary model building [5,6].The F-term hybrid inflation in a supersymmetric high energy model with gauge symmetry G has a renormalizable superpotential W and a canonical Kähler potential K [7,8]. In particular, the Z 2 R-parity in the supersymmetric SMs (SSMs) is extended to a continuous U (1) R symmetry, which determines superpotential. With the minimal W and K , the gauge symmetry G is broken down to a subgroup H at the end of inflation. For the supersymmetric high energy model, in general, we can consider either a left-right model with gauge symmetry [9,10]. H can be the SM or SM-like gauge group, etc.In the supersymmetric hybrid inflation [7], 1 the quantum corrections arising from supersymmetry breaking drive inflation, and the scalar spectral index was predicted to be n s = 1 − 1/N 0.98, where N = 60 denotes the number of e-foldings necessary to resolve the horizon and f...