Molybdenum nitride films with the NaCl structure (B1-MoN) were epitaxially grown on α- Al2 O3 (001) and MgO(001) substrates at 973 K by pulsed laser deposition (PLD) under nitrogen radical irradiation. The highly crystalline epitaxial films enabled us to determine the three-dimensional cell parameters, which was motivated by theoretical calculations that B1-MoN, a predicted superconductor, is elastically unstable against tetragonal and trigonal distortions. On α- Al2 O3 (001), the B1-MoN phase (composition, Mo1 N0.98) was grown with its (111) planes parallel to the substrate surface. X-ray diffraction analysis with a multiaxes diffractometer detected only a small trigonal lattice distortion [a=0.4219(3) nm, α=89.28(5)°] with an expansion along the [111] direction perpendicular to the substrate surface. The film grown on MgO(001) had the MoN1.03 composition and showed a slight tetragonal distortion (a=0.4213 and c=0.424 nm) due to fitting to the MgO substrate lattice (a=0.4213 nm). These two stoichiometric films showed no superconductivity above 2 K. A lower nitrogen content (MoN0.86) film was obtained on α- Al2 O3 (001) using a higher deposition rate. The corresponding film had a much smaller lattice constant [a=0.4184(3) nm], and a similar distortion [α=89.41(5)°]. The B1- MoN0.86 film showed superconductivity with a transition temperature Tc =4.2 K. The suppression of the superconductivity of the former stoichiometric phase can be interpreted in terms of the lattice expansion.