Abstract: We study a holographic superconductor model with momentum relaxation due to massless scalar fields linear to spatial coordinates(ψI=βδIixi), where β is the strength of momentum relaxation. In addition to the original superconductor induced by the chemical potential(μ) at β=0, there exists a new type of holographic superconductor induced by β even at μ=0. After analysing ground states and phase diagrams for various β/μ, we study optical electric(σ), thermoelectric(α), and thermal(κ¯) conductivities. When the system undergoes a phase transition from normal to a superconducting phase, 1/ω pole appears in the imaginary part of the electric conductivity, implying infinite DC conductivity. We discuss some properties related to the conductivities including the coherent/incoherent metal transition, Ferrell-Glover-Tinkham (FGT) sum rule, Homes' law, and Ward identities.