  We study a nonsingular bounce inflation model, which can drive the early
universe from a contracting phase, bounce into an ordinary inflationary phase,
followed by the reheating process. Besides the bounce that avoided the Big-Bang
singularity which appears in the standard cosmological scenario, we make use of
the Horndesky theory and design the kinetic and potential forms of the
lagrangian, so that neither of the two big problems in bouncing cosmology,
namely the ghost and the anisotropy problems, will appear. The cosmological
perturbations can be generated either in the contracting phase or in the
inflationary phase, where in the latter the power spectrum will be
scale-invariant and fit the observational data, while in the former the
perturbations will have nontrivial features that will be tested by the large
scale structure experiments. We also fit our model to the CMB TT power
spectrum.
