Transient blade loading limits the lifetime of turbocharger turbine blades. This study investigates the flutter instability of a radial turbocharger turbine blade under pulsating inlet conditions. The viscous Navier-Stokes equations with the SST-kω turbulence model and curvature correction were solved. A time-marching 3D finite volume method was used in the CFX17 CFD solver to model the vibrating blade in a traveling wave mode applying Fourier Transformation. For flutter calculations, moving boundaries with specified modal displacements were used. An area of instability was recognized on the suction-side of the rotor blade. FSI steady-state analysis was then performed to assess the effects of shock position and blade profile on the blade stability in the recognized vulnerable region. The results show that a higher trailing edge radius increases the stability and leads to a significant reduction of flutter risk whereas the maximum thickness and leading-edge radius do not notably affect the flutter occurrences.