The modified Chaplygin gas (MCG) as an interacting model of holographic dark energy in which dark energy and dark matter are coupled together is investigated in this paper. Concretely, by studying the evolutions of related cosmological quantities such as density parameter Ω, equation of state w, deceleration parameter q and transition redshift z T , we find the evolution of the universe is from deceleration to acceleration, their present values are consistent with the latest observations, and the equation of state of holographic dark energy can cross the phantom divide w = −1. Furthermore, we put emphasis upon the geometrical diagnostics for our model, i.e., the statefinder and Om diagnostics. By illustrating the evolutionary trajectories in r − s, r − q, w -w and Om planes, we find that the holographic constant c and the coupling constant b play very important roles in the holographic dark energy (HDE) model. In addition, we also plot the LCDM horizontal lines in Om diagrams, and show the discrimination between the HDE and LCDM models. modified Chaplygin gas, interacting holographic dark energy, geometrical diagnostics PACS: 98.80.Es, 98.80.JkIt has been believed that the universe is undergoing a phase of accelerated expansion, which is indicated by such astronomical observations as Type Ia supernovae (SNe) [1], cosmic microwave background (CMB) anisotropy [2] and large scale structure (LSS) [3]. This implies that there is a mysterious component in the universe, which has a large negative pressure called dark energy (DE). The Wilkinson Microwave Anisotropy Probe (WMAP) satellite experiment indicates that the universe is spatially flat on a large scale, and the dark energy, dark matter (DM) and baryon matter in the universe make up about 73%, 23%, and 4%, respectively. Recently, there are some studies showing that the equation of state (EoS) of dark energy w X = p X ρ X might evolve from w X > −1 to w X < −1. When these SNe results are combined with WMAP 5-year data the 95% confidence limits on an unevolving EoS are −1.11 < w 0X < −0.86 [4]. More and more scenarios have been proposed as the candidates of DE to explain the accelerated expansion. What fits best with the observational data is the cosmological constant λ [5], which has the EoS w = −1, and is called the LCDM model in which *Corresponding author (email: ybwu61@163.com) the cosmological constant is combined with the cold dark matter. However, it is plagued with some problems, i.e., the "cosmic coincidence" problem [6] and the "fine tuning" problem [7]. A number of scalar field models have been constructed, such as quintessence [8], phantom [9], K-essence [10], quintom [11] and tachyon [12]. Furthermore, models such as Chaplygin gas (CG) [13] and modified Chaplygin gas (MCG) [14][15][16], which attempt to unify DE and DM, are proposed by allowing for a fluid with an EoS which evolves between the both.In recent years, the model has been stimulated by the holographic principle, i.e., the so-called holographic dark energy (HDE) has been put forward by Li...