Grassmannian frames consist of unit-norm vectors with a maximum cross correlation between each other that is minimal. A property like that is desired in many applications, such as in wireless communications, sparse recovery, quantum information theory, and more. In this letter, we present an iterative algorithm targeting the construction of Grassmannian frames, based on a collision-based packing of equal-radius hyperspheres on the surface of a unit-norm hypersphere. Our results show that the algorithm is capable of producing frames with very low coherence, and at a fast convergence rate compared to other methods.