For various densities of gas jets including very light hydrogen and relatively heavy ones, the penetration length and diffusion process of a single high-speed gas fuel jet injected into air are computed by performing a large eddy simulation (LES) with fewer arbitrary constants applied for the unsteady three-dimensional compressible Navier-Stokes equation. In contrast, traditional ensemble models such as the Reynolds-averaged Navier-Stokes (RANS) equation have several arbitrary constants for fitting purposes. The cubic-interpolated pseudo-particle (CIP) method is employed for discretizing the nonlinear terms. Computations of single-component nitrogen and hydrogen jets were done under initial conditions of a fuel tank pressure of gas fuel = 10 MPa and back pressure of air = 3.5 MPa, i.e., the pressure level inside the combustion chamber after piston compression in the engine. An important point of the present study is to obtain clear evidence for Hamamoto’s experimental data that the penetration length of a light hydrogen gas jet of low density is nearly the same as that of relatively heavy gas jets such as nitrogen or carbon dioxide. It is confirmed that the computed penetration lengths of hydrogen and nitrogen gas jets injected into air are nearly the same, although hydrogen has very small inertia due to its low density. It is also stressed that computational results agree fairly well with Hamamoto’s empirical data on penetration lengths and diffusion area in the direction normal to the jet axis. Moreover, computations based on the present LES also clarify a physical mechanism underlying combustion instability in engine experiments conducted by Takagi et al., although the RANS is relatively difficult to reveal instability of unsteady flow field.