This paper proposes a novel, noniterative reconstruction method for magnetic resonance electrical properties tomography (MREPT). For this method, we first estimate the electric field using a novel, three-dimensional integral equation, derived from Maxwell's equations and vector calculus identities. The EPs are then reconstructed from the estimated electric field, using Ampere’s law. Our method can estimate an arbitrary three-dimensional distribution of EPs, including those varying in the z-axis. The efficacy of our proposed method was validated through numerical simulations and a phantom experiment.