Waveform light detection and ranging detection (LiDAR) systems capture the entire backscattered signal from the interaction of the laser beam with objects located within the laser footprint. The target response (TR) is a time-dependent curve implying the geophysical attribute of the detected objects. TR restoration by removing the effect of the system waveform (SW) from the received waveform is crucial but suffers from ill-posedness. We recast the deconvolution problem to a nonlinear least squares problem and use the proposed method to deal with the LiDAR waveforms with negative tails. The proposed method is an iterative algorithm starting with a practical initial TR seen as the combination of parts of the deconvolution results obtained by the L1- and L2-regularization methods, then ending by a stopping criteria set empirically. A set of hybrid LiDAR waveforms constructed by the SW of our LiDAR and the synthetic TRs are employed to evaluate the performance of the TR retrieval. The results show the superior performance of the proposed method in both reconstructions of the flattened and sharp curves of the TRs as compared to the L1- and L2-regularization methods. This demonstrates the potential of the nonlinear least squares method for retrieving the range and geometric physical information from the LiDAR waveforms.