We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, L3, using the identification of L3 with C × R. Further we give a different proof for the singular Björling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surface which contains a given curve and has a special singularity. © 2018 International Society for Photogrammetry and Remote Sensing. All Rights Reserved.