There is a need for the development of lumped-parameter models that can be used for real-time control design and optimization for laser-based additive manufacturing (AM) processes. Our prior work developed a physics-based multivariable model for melt–pool geometry and temperature dynamics in a single-bead deposition for a directed energy deposition process and then validated the model using experimental data from deposition of single-bead Ti–6AL–4V (or Inconel^{®}718) tracks on an Optomec^{®} Laser Engineering Net Shaping (LENS^{™}) system. In this paper, we extend such model for melt–pool geometry in a single-bead deposition to a multibead multilayer deposition and then use the extended model on melt–pool height dynamics to predict part height of a three-dimensional build. Specifically, the extended model incorporates temperature history during the build process, which is approximated by super-positioning the temperature fields generated from Rosenthal's solution of point heat sources, with one heat source corresponding to one bead built before. The proposed model for part height prediction is then validated using builds with a variety of shapes, including single-bead thin wall structures, a patch build, and L-shaped structures, all built with Ti–6AL–4V using an Optomec^{®} LENS^{TM} MR-7 system. The model predictions on average part height show reasonable agreement with the measured average part height, with error rate less than 15%.