We propose a single-photon router using a single atom with an inversion center coupled to quantum multichannels made of coupled-resonator waveguides. We show that the spontaneous emission of the atom can direct single photons from one quantum channel into another. The on-demand classical field perfectly switches off the single-photon routing due to the quantum interference in the atomic amplitudes of optical transitions. Total reflections in the incident channel are due to the photonic bound state in the continuum. Two virtual channels, named the scatter-free and controllable channels, are found, which are coherent superpositions ofquantumchannels.Anyincidentphotoninthescatter-freechannelistotallytransmitted.Thepropagatingstates of the controllable channel are orthogonal to those of the scatter-free channel. Single photons in the controllable channel can be perfectly reflected or transmitted by the atom.