Labyrinth weirs bearing longer crest lengths than linear weirs in the available approach channel width offer significant flow magnification. Triangular, rectangular, and trapezoidal shapes of labyrinth weirs have been studied in the past few decades. A staged labyrinth weir having multiple crest elevations helps modify the outflow hydrograph for extreme storms. Being less efficient at lower heads, these structures facilitate the use of reservoir volume and allow flows downstream through staged crests. The discharge coefficient depends on crest shape, head-to-weir height ratio, apex configuration, crest thickness, and sidewall angle. The present study aims to determine the discharge coefficient of a staged trapezoidal labyrinth weir using a Support Vector Machine (SVM) and Nonlinear Regression (NLR) approaches. In the present study, 133 laboratory data from the literature were utilized to generate discharge coefficient prediction models using different combinations of pertinent parameters. A discharge coefficient equation based on the NLR approach and an assessment of its accuracy with earlier reported predictors is presented herein.