  The diffusion behavior of particles moving in complex heterogeneous
environment is a very topical issue. We characterize particle's trajectory via
an underdamped Langevin system driven by a Gaussian white noise with a time
dependent diffusivity of velocity, together with a random relaxation timescale
$\tau$ to parameterize the effect of complex medium. We mainly concern how the
random parameter $\tau$ influences the diffusion behavior and ergodic property
of this Langevin system. Besides, the comparison between the fixed and random
initial velocity $v_0$ is conducted to show the effect of different initial
ensembles. The heavy-tailed distribution of $\tau$ with finite mean is found to
suppress the decay rate of the velocity correlation function and promote the
diffusion behavior, playing a competition role to the time dependent
diffusivity. More interestingly, a random $v_0$ with a specific distribution
depending on random $\tau$ also enhances the diffusion. Both the random
parameters $\tau$ and $v_0$ influence the dynamics of the Langevin system in an
non-obvious way, which cannot be ignored even they has finite moments.
