In the condition of linear dispersion relation, the quantum entanglement between two atoms placed paratactically in a one-dimensional waveguide is investigated. In order to investigate the entanglement degree between the two atoms, the transmission and reflection spectra amplitudes are calculated by using the real-space method, and the single-photon scattering properties and concurrence of the entangled states are discussed. Results show that the scattering spectra of Fano line shape occur by changing the atomic dipole-dipole interaction. The dipole-dipole interaction may be utilized as a possible tool to lead to spectral Fano resonance. The quantum concurrence can also occur Fano resonance by controlling the atom-waveguide coupling strength, and the maximum quantum entanglement can be inferred by observing Fano resonance.