Abstract: One of the key factors regarding the validity of the results of discontinuous deformation analysis (DDA) is the computational accuracy of the contact force. The classic DDA employs a penalty function to enforce the contact constraints between blocks, which is easy to implement but challenging to choose the penalty value in the actual computation. To overcome the limitation, a three-dimensional (3-D) DDA based on an optimized augmented Lagrangian method (ALM), abbreviated as DDA-3a, is established to modify the treatment of the contact constraints. This study provides necessary knowledge to fully implement and further optimize the ALM in the 3-D DDA by integrating it with the open-close iteration, and an adaptive penalty update scheme. Numerical examples are designed to exhibit the capability of DDA-3a in the computational accuracy, efficiency, and robustness. This study reveals that the DDA-3a can be used to analyze the discontinuous mechanical behavior of polyhedral block systems, such as the stability analysis of jointed rock-masses.