Li2IrSi3 crystallizes to a novel trigonal structure with the space group P31c, which consists of an alternate stacking of planar silicon kagome planes and Li and Ir planes. The structure is weakly noncentrosymmetric owing to the displacement of kagome planes along the c-axis and the staggered rotation of silicon triangles in the kagome planes. Superconductivity at 3.8 K was discovered in Li2IrSi3. Weakened inversion symmetry breaking, together with the increased electronic DOS at the Fermi level, plays a key role in the superconductivity of Li2IrSi3. We aim to perform the muon-spin rotation (µSR) study, both transverse field (TF) and zero field (ZF) to investigate microscopic superconducting properties of Li2IrSi3. TF µSR provides measurements for superconducting Gap structure. ZF µSR is important to know time reversal symmetry of the superconducting state is broken or preserved.