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We use observational data from Type Ia Supernovae (SN), Baryon AcousticOscillations (BAO), Cosmic Microwave Background (CMB) and observational Hubbledata (OHD), and the Markov Chain Monte Carlo (MCMC) method, to constrain thecosmological scenario of holographic dark energy with varying gravitationalconstant. We consider both flat and non-flat background geometry, and wepresent the corresponding constraints and contour-plots of the modelparameters. We conclude that the scenario is compatible with observations. In1$\sigma$ we find $\Omega_{\Lambda0}=0.72^{+0.03}_{-0.03}$,$\Omega_{k0}=-0.0013^{+0.0130}_{-0.0040}$, $c=0.80^{+0.19}_{-0.14}$ and$\Delta_G\equiv G'/G=-0.0025^{+0.0080}_{-0.0050}$, while for the present valueof the dark energy equation-of-state parameter we obtain$w_0=-1.04^{+0.15}_{-0.20}$.

Observational constraints on holographic dark energy with varying gravitational constant