Control of part geometry to achieve desired geometric accuracy is critical for fabrication of complex components via laser-based additive manufacturing (AM) processes. Especially for Laser Powder Bed Fusion (LPBF) AM, which uses laser heat source with a much smaller focus diameter and builds parts with much finer resolution, the requirement on geometric accuracy poses additional challenges. For example, simulating a LPBF process using finite-element analysis (FEA) requires significantly higher computation power and time compared to simulating other AM processes such as the direct energy deposition (DED) processes, which makes FEA models difficult to use for real-time control and/or optimization. This paper aims to develop an analytical, control-oriented model on the dynamics of melt-pool volume in building a multi-track part using LPBF. The derivation of the melt-pool dynamics starts from a lumped-parameter-based governing equation on the energy balance of the molton puddle, combined with characterization of thermal history and temperature contributions from past tracks. Based on this analytical model on melt-pool volume, a nonlinear inverse-dynamics controller is designed to adjust laser power such that the melt-pool volume is regulated to a constant set point during the build process of a multi-track part. The performance of the control is evaluated by FEA using Autodesk’s Netfabb Local Simulation. This proof-of-concept study lays the initial foundation for developing more advanced control-oriented models for melt-pool geometry in LPBF and future work includes experimental evaluation of the proposed modeling and control design.