This study presents an electrical impedance tomography (EIT) method for reconstructing the electrical conductivity of early-age concrete, with a particular focus on its temporal evolution during the hydration process. The proposed method estimates the electrical properties of concrete, including electrical conductivity and resistivity, by minimizing a cost functional defined as the misfit between measured and computed electric potentials at surface-mounted electrodes. The forward problem is formulated using the complete electrode model, in which the Laplace equation governing the electric potential is solved while accounting for electrode contact impedance and prescribed current injection. The inverse problem is posed as a partial differential equation (PDE)-constrained optimization problem, where the governing equations and boundary conditions are enforced as constraints. This constrained optimization problem is transformed into an unconstrained formulation using the Lagrange multiplier method, and the electrical conductivity distribution is iteratively updated from an initial estimate until the first-order optimality conditions are satisfied. To experimentally validate the proposed method, electric potentials were measured at surface electrodes on mortar specimens under controlled current injection. These measurements were inverted to reconstruct the electrical conductivity distributions of the specimens. Inverse analyses were conducted using data acquired at multiple hydration stages and with different initial conductivity estimates. The reconstruction results consistently converged to similar conductivity distributions, regardless of the initial estimates, demonstrating the stability and robustness of the proposed EIT method. The proposed approach is applicable to the nondestructive evaluation of concrete structures and to the real-time monitoring of early-age hydration processes.