Nonthermal particles can be produced due to incomplete thermalization at collisionless shocks and further accelerated to very high energies via diffusive shock acceleration. In a previous study we explored the cosmic ray (CR) acceleration at cosmic shocks through numerical simulations of CR modified, quasi-parallel shocks in 1D plane-parallel geometry with the physical parameters relevant for the shocks emerging in the large scale structure formation of the universe (Kang & Jones 2002). Specifically we considered pancake shocks driven by accretion flows with

and the preshock gas temperature of

. In order to consider the CR acceleration at shocks with a broader range of physical properties, in this contribution we present additional simulations with accretion flows with

and

. We also compare the new simulation results with those reported in the previous study. For a given Mach number, shocks with higher speeds accelerate CRs faster with a greater number of particles, since the acceleration time scale is

. However, two shocks with a same Mach number but with different shock speeds evolve qualitatively similarly when the results are presented in terms of diffusion length and time scales. Therefore, the time asymptotic value for the fraction of shock kinetic energy transferred to CRs is mainly controlled by shock Mach number rather than shock speed. Although the CR acceleration efficiency depends weakly on a well-constrained injection parameter,

, and on shock speed for low shock Mach numbers, the dependence disappears for high shock Mach numbers. We present the 'CR energy ratio',

, for a wide range of shock parameters and for

= 0.2 - 0.3 at terminal time of our simulations. We suggest that these values can be considered as time-asymptotic values for the CR acceleration efficiency, since the time-dependent evolution of CR modified shocks has become approximately self-similar before the terminal time.