In the present work both the (alpha,gamma) and (p,gamma) cross sections on the p-nucleus Cd-106 have been measured in the energy range relevant to the astrophysical p-process. The results are compared with the predictions of the statistical model calculations implemented with the NON-SMOKER code using different input parameters. The proton capture cross section has also been measured for Cd-108. The alpha + Cd-106 optical potential, an important input parameter for the Cd-106(alpha,gamma) reaction rate determination, can be determined directly by measuring the deviation from the Rutherford scattering in the Cd-106(alpha,alpha)Cd-106 elastic scattering experiment. This experiment has also been performed in a wide angular range and the results are compared with different global optical potentials.