We investigate the electrical conductivity (σ) of quark matter via the Kubo formula at finite temperature and zero quark density (T = 0, µ = 0) in the presence of an external strong magnetic field. For this purpose, we employ the dilute instanton-liquid model, taking into account its temperature modification with the trivial-holonomy caloron distribution. By doing that, the momentum and temperature dependences for the effective quark mass and model renormalization scale are carefully evaluated. From the numerical results, it turns out that σ ≈ (0.02 ∼ 0.15) fm −1 for T = (0 ∼ 400) MeV with the relaxation time τ = (0.3 ∼ 0.9) fm. In addition, we also parameterize the electrical conductivity as σ/T ≈ (0.46, 0.77, 1.08, 1.39) CEM for τ = (0.3, 0.5, 0.7, 0.9) fm, respectively. These results are well compatible with other theoretical estimations, including those from the lattice QCD simulations. It also turns out that the external magnetic field plays only a minor role for σ even for the very strong one B0 ∼ m 2 π × 10 and becomes relatively effective for T 200 MeV. Moreover, we compute the soft photon emission rate from the quark-gluon plasma, using the electrical conductivity calculated.