The electronic structure and spin-dependent conductance of a magnetic junction consisting of two Fe-doped carbon nanotubes and a C60 molecule are investigated using a first-principles approach that combines the density functional theory with the nonequilibrium Greens function technique. The tunneling magnetoresistance ratio is found to be 11%. The density of states and transmission coefficient through the molecular junction are analyzed and compared to layered magnetic tunneling junctions. Our findings suggest new possibilities for experiments and for future technology.