Potassium nitrate and sorbitol (KNSB) is a promising low-cost solid propellant for aerospace, characterized by stable combustion and a low pressure exponent. However, its application is constrained by a deficiency in detailed numerical simulation studies for solid rocket motors (SRMs). This study develops a comprehensive numerical model for a KNSB SRM, incorporating dynamic mesh techniques to simulate real-time burning surface regression. Steady-state internal flow field analysis proves to be well-validated by literature data, with combustion pressure and thrust errors of 7.7% and 3.2%, respectively. Increasing oxidizer mass fraction from 57.5% to 70% leads to a significant temperature rise of 22.15%. Dynamic simulations reveal that thrust and pressure initially increase after ignition but later decline as the regressing surface reduces gas generation below the nozzle exhaust rate. Comparison with literature yields an average thrust error of 4.9%, with simulated trends matching documented behavior well. This research provides a robust reference for performance prediction and supports further development of KNSB SRMs.