The classical full-waveform inversion is a method for obtaining detailed velocity models of the subsurface, formulated as an inverse problem, in which modeling and adjoint operators use the two-way wave equation. Solving the wave equation with the two-way propagator is computationally demanding when compared to the less accurate one-way propagator. However, the range of validity of the one-way wave equation is quite reasonable for most of the geological environments in which exploration has been carried out. For these situations, we propose to perform full-waveform inversion based on the first-order Born approximation, using the one-way propagator which promises to be less computationally intensive than the classical FWI. Our approach includes defining the objective function by cross-correlation to mitigate the impacts that cycle-skipping and amplitude differences have on the solution, and improving the gradient information by deconvolving and integrating the back-propagated residuals to accelerate convergence.