A model is suggested to unify the Einstein general relativity and Dirac cosmology. There is one adjusted parameter b2 in our model. After adjusting the parameter b2 in the model by using the supernova data, we have calculated the gravitational constant \skew3\bar G and the physical quantities a(t), q(t) and ρr(t)/ρb(t) by using the present day quantities as the initial conditions and found that the equation of state parameter wθ equals -0.83, the ratio of the density of the addition creation ΩΛ = 0.8 and the ratio of the density of the matter including multiplication creation, radiation and normal matter Ωm = 0.2 at present. The results are self-consistent and in good agreement with present knowledge in cosmology. These results suggest that the addition creation and multiplication creation in Dirac cosmology play the role of the dark energy and dark matter, respectively. We have shown that our theory is consistent with solar system tests.