This paper describes an efficient edge-preserved regularization algorithm for downward continuation of magnetic data in detection of unexploded ordnance (UXO). The magnetic anomalies arising from multi-source UXO can overlap at a height over the ground surface, while causative sources may not be readily separated due to low level of signal-to-noise ratio of the observed data. To effectively the magnetic method work in the cleanup stage of contaminated area with UXO, the magnetic anomalies of UXO sources should be enhanced in order to separate the locations of different sources. The stable downward continuation of magnetic data can increase the signal-to-noise ratio which subsequently causes the separation of UXO sources by enhancing the signals. We formulate the downward continuation as a linear ill-posed deconvolution problem in this study. To obtain a reasonable downward continued field, it is stabilized in a Fourier domain to regularize the downward solution using the edge-preserved (or total-variation) algorithm. The L-curve method is used to choose the optimum value of the regularization parameter which is a trade-off between the misfit and the solution norms in the cost function of optimization problem. A synthetic magnetic field is constructed from isolated multi-source UXO anomalies, whose results show that the data can be stably downward continued by the proposed method. Likewise, a field data set has been provided to demonstrate the capability of the applied method in UXO detection.