In this paper the vacuum energy scenario (or time-dependent cosmological constant) from the renormalization group (RG) equation is studied. By considering the renormalization group scale described by the Hubble parameter, we apply the current observational data to constrain this RG dark energy model. Concretely, the different combinations of cosmic observational data, including the kinematical and the dynamical part, are investigated to constrain the RG model. For comparison we also consider the cosmic constraints on the dark model by taking the Ricci scalar as the renormalization group scale. In addition, we compare these two RG dark energy models with the cosmological constant.
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