The superconducting gap structure of a charge density wave (CDW) superconductor LaPt2Si2 (Tc = 1.6 K) having a quasi two dimensional crystal structure has been investigated using muon spin rotation/relaxation (µSR) measurements carried out in transverse field (TF), zero field (ZF) and longitudinal field (LF) geometries. Rigorous analysis of TF-µSR spectra in the superconducting state corroborates that the temperature dependence of the effective penetration depth, λL, derived from muon spin depolarization, fits to an isotropic s + s−wave model suggesting that the Fermi surface contains two gaps of different magnitude rather than an isotropic gap expected for a conventional s−wave superconductor. On the other hand, ZF µSR data do not show any significant change in muon spin relaxation rate above and below the superconducting transition indicating the fact that time-reversal symmetry is preserved in the system.