Antiperovskites are a promising candidate structure for the exploration of new materials. We discovered an antiperovskite phosphide, LaPd3P, following our recent synthesis of APd3P (A = Ca, Sr, Ba). While APd3P and (Ca,Sr)Pd3P were found to be tetragonal or orthorhombic systems, LaPd3P is a new prototype cubic system (a = 9.0317(1) Å) with a noncentrosymmetric space group (I4̅3m). LaPd3P exhibited superconductivity with a transition temperature (Tc) of 0.28 K. The upper critical field, Debye temperature, and Sommerfeld constant (γ) were determined to be 0.305(8) kOe, 267(1) K, and 6.06(4) mJ mol-1 K-2 f.u.-1, respectively. We performed first-principles electronic band structure calculations for LaPd3P and compared the theoretical and experimental results. The calculated Sommerfeld constant (2.24 mJ mol-1 K-2 f.u.-1) was much smaller than the experimental value of γ because the Fermi energy (EF) was located slightly below the density of states (DOS) pseudogap. This difference was explained by the increase in the DOS at EF due to the approximately 5 atom % La deficiency (hole doping) in the sample. The observed Tc value was much lower than that estimated using the Bardeen-Cooper-Schrieffer equation. To explain the discrepancy, we examined the possibility of an unconventional superconductivity in LaPd3P arising from the lack of space inversion symmetry.