We propose a scheme to implement the phase-robust topological router based on a one-dimensional dimerized superconducting circuit lattice with long-range hopping. We show that the proposed dimerized superconducting circuit lattice can be mapped into an extended chiral-symmetric Su-Schrieffer-Heeger (SSH) model with long-range hopping, in which the existence of long-range hopping induces a special zero-energy mode. The peculiar distribution of the zero-energy mode enables us to engineer a phase-robust topological router, which can achieve quantum state transfer (QST) from one site (input port) to multiple sites (output ports). Benefiting from the topological protection of chiral symmetry, we demonstrate that the presence of the mild disorder in nearest-neighbor and long-range hopping has no appreciable effects on QST in the lattice. Especially, after introducing another new long-range hopping into the extended SSH lattice, we propose an optimized protocol of the phase-robust topological router, in which the number of the output ports can be efficiently increased. Resorting to the Bose statistical properties of the superconducting circuit lattice, the input port and output ports assisted by the zero-energy mode can be detected via the mean distribution of the photons. Our work breaks the traditional QST form with only one outport by the zero-energy mode and opens a pathway to construct large-scale quantum information processing in the SSH chains with long-range hopping., Comment: 15 pages, 12 figures