We compute the evolution of open, but spatially flat, cold dark matter (CDM) models with a cosmological constant (Ω + ∆ = 1) containing both baryonic matter and dark matter. Hydrodynamics is treated with a highly developed Eulerian hydrodynamic code (see Cen 1992). A standard particle-mesh (PM) code to calculate the motion of collisionless particles is coupled with this hydrodynamic code. We adopt the following parameters: h ≡ H0/100 km s-1 Mpc-1 = ⅔, Ω = 0.3, λ = 0.7, Ωb = 0.034 with amplitude of the perturbation spectrum fixed by the COBE DMR measurements (Smoot et al. 1992) being sun8 = 0.67. Three different boxes are simulated with box sizes of L = (64, 16, 4) h-1 Mpc, respectively, the smallest box providing good resolution but little valid information due to the absence of large-scale power. We use 1283 = 106.3 baryonic cells and an equal number of dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H+ He, He+, He++, e-) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zel'dovich-Sunyaev γ parameter is estimated to be γbar = (3.6±1.8) × 10-7, below currently attainable observations, with a rms fluctuation of approximately (δbarγ= (4.0±2.0) × 10-7 on arcminute scales.The rate of galaxy formation peaks at a relatively earlier epoch (Ζ ∼ 2.0) than in the standard (Ω = 1) CDM model (Ζ ∼ 0.5) . With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of mb = 109.5 Msun with a reasonable fit to the Schechter luminosity function if the baryon mass to blue light ratio is approximately 4. In addition, one very large PM simulation was made in a box with size (400 h-1 Mpc) containing 2503 = 107.2 particles. Utilizing this simulation we find that the model yields a cluster mass function and a cluster-cluster correlation function which are in good agreement with observations. The one-dimensional pair- wise velocity dispersion is 380 km s-1 at 1 h-1 separation, in agreement with Davis & Peebles (1983). The velocity autocorrelation function has a coherence length of 110 h-1 Mpc, much larger (× 4) than that in the standard CDM model and in better agreement with observed large coherent flows. A preliminary estimate of strong gravitational lensing statistics in this model (cf. Cen et al. 1993) indicates that, despite the greater pathlength due to ∆ > 0, the model is consistent with observations with regard to large angle splittings events; the number expected (for ∆θ > 8") is, by an order of magnitude, less than for standard, COBE normalized CDM. Overall the model is more successful than standard biased CDM both on large scales with regard to the coherent motion (a larger coherent length in this model) and on small scales with regard to velocity dispersion (a smaller one-dimensional pairwise velocity dispersion in much better agreement with observation), and with regard to earlier formation of galaxies and structure than in the standard CDM model.