Scale-free networks are structures, whose nodes have degree distributions that follow a power law. Here we focus on the dynamics of semiflexible scale-free polymer networks. The semiflexibility is modeled in the framework of [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], which allows for tree-like networks with arbitrary architectures to include local constrains on bond orientations. From the wealth of dynamical quantities we choose the mechanical relaxation moduli (the loss modulus) and the static behavior is studied by looking at the radius of gyration. First we study the influence of the network size and of the stiffness parameter on the dynamical quantities, keeping constant γ, a parameter that measures the connectivity of the scale-free network. Then we vary the parameter γ and we keep constant the size of the structures. This fact allows us to study in detail the crossover behavior from a simple linear semiflexible chain to a star-like structure. We show that the semiflexibility of the scale-free networks clearly manifests itself by displaying macroscopically distinguishable behaviors.