Various core designs with multi -batch fuel management (FM) are proposed and optimized for an innovative small modular reactor (iSMR), focusing on enhancing the inherent safety and neutronic performance. To achieve soluble -boron -free (SBF) operation, cylindrical centrally -shielded burnable absorbers (CSBAs) are utilized, reducing the burnup reactivity swing in both two- and three -batch FMs. All 69 fuel assemblies (FAs) are loaded with 2 -cylindrical CSBA. Furthermore, the neutron economy is improved by deploying a truly -optimized PWR (TOP) lattice with a smaller fuel radius, optimized for neutron moderation under the SBF condition. The fuel shuffling and CSBA loading patterns are proposed for both 2- and 3 -batch FM with the aim to lower the core leakage and achieve favorable power profiles. Numerical results show that both FM configurations achieve a small reactivity swing of about 1000 pcm and the power distributions are within the design criteria. The average discharge burnup in the two -batch core is comparable to three -batch commercial PWR like APR -1400. The proposed checker -board CR pattern with extended fingers effectively assures cold shutdown in the two -batch FM scenario, while in the three -batch FM, three N-1 scenarios are failed. The whole evaluation process is conducted using Monte Carlo Serpent 2 code in conjunction with ENDF/B-VII.1 nuclear library.