In this paper we study the primordial perturbations generated in an inflation model in which the period of inflation is preceded by a cosmological bounce. After reviewing the background evolution in this model we study the resulting curvature perturbations, entropy fluctuations and non-Gaussianities. Our results show that both the power spectrum of curvature perturbations and the spectra describing the non-Gaussianities obtain oscillatory features. Next, we calculate the tensor perturbations in this model and find a valley in its spectrum. This is a generic feature of inflationary models with a bounce. Further observational signatures and theoretical implications of the model are discussed.