In this talk, we explore an idea of having Newton's constant change its value depending on the curvature scale involved. Such modification leads to a scalar-tensor gravity theory, with the Lagrangian derived from renormalization group flow arguments. Assuming running of the (classical) gravitational coupling is described by the same beta function as the (quantum) one in QCD, one is lead to a simple f(R)-type model with several striking features. The model has unique de Sitter attractor, with effective cosmological constant exponentially suppressed relative to Planck scale by inverse of the running parameter. Thus not only cosmological constant appears dynamically in this model, its value is small precisely because the gravity we observe is almost Einstein-like. With the same number of parameters as Lambda-CDM and no excessively small numbers involved, this looks like an interesting cosmological model, and we investigate its dynamics and observational consequences. This talk is mainly based on arXiv:1101.4995v1 [astro-ph.CO].