In this paper, the PDS-XADS LBE-cooled core open-loop transfer function was calculated by considering the source importance in point-kinetic equations. For this purpose, the overall-feedback transfer function was calculated considering the lumped-model for 14-steps of subcritical levels. Following effects were considered in three steps: 1. Doppler broadening, fuel expansion, coolant density and structure expansion, 2. Delayed-reactivity and void-worth inserted to prior step, 3. Severe-accident condition, inserted to prior steps. The linear stability analysis was modeled by using the Bode diagrams, Nyquist stability criterion and Nichols chart in MATLAB for each subcritical level and six groups of delayed neutrons. For optimized subcritical level determination, a conservative severe accident was considered. According to calculation results and analysis, the PDS-XADS core is stable and in optimized subcritical level, has the higher safety margin. The results are in good agreement with SIMMER-III code and main neutronic results. The optimized subcritical level by using the lumped-model is 0.97687.