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We constrain holographic dark energy (HDE) with time varying gravitationalcoupling constant in the framework of the modified Friedmann equations usingcosmological data from type Ia supernovae, baryon acoustic oscillations, cosmicmicrowave background radiation and X-ray gas mass fraction. Applying a MarkovChain Monte Carlo (MCMC) simulation, we obtain the best fit values of the modeland cosmological parameters within $1\sigma$ confidence level (CL) in a flatuniverse as: $\Omega_{\rm b}h^2=0.0222^{+0.0018}_{-0.0013}$, $\Omega_{\rm c}h^2=0.1121^{+0.0110}_{-0.0079}$, $\alpha_{\rm G}\equiv \dot{G}/(HG)=0.1647^{+0.3547}_{-0.2971}$ and the HDE constant$c=0.9322^{+0.4569}_{-0.5447}$. Using the best fit values, the equation ofstate of the dark component at the present time $w_{\rm d0}$ at $1\sigma$ CLcan cross the phantom boundary $w=-1$.

Observational constraints on G-corrected holographic dark energy using a Markov chain Monte Carlo method