Carbonate reservoirs are important targets for promoting the oil and gas reserve exploration and production in China. However, such reservoirs usually contain the developed complex pore structures, which heavily affect the precision in seismic prediction of petrophysical parameters. As one of the most important parameters to characterize reservoir rock, pore parameters can not only describe the pore structure, but also be used to evaluate the oil/gas bearing capabilities of potential reservoirs. The conventional rock-physics models (such as the Gassmann model) are established under the assumption of fully-connected pores, which cannot reasonably describe the geometrical complexity of real rocks. To characterize the effects of different pore types on the elastic moduli, this work proposes a rock-physics modeling method for carbonates, where the volume content of connected pores (defined as the pore-connectivity parameter) is quantified. The proposed method treats the pore-connectivity parameter as an objective parameter to characterize the spatial variations of pore structure. Specifically, the method combines the differential equivalent medium theory and the Gassmann model, and derives a linearized forward operator to quantitatively relate porosity, fluid saturation, and pore-connectivity parameter to the seismic elastic parameters. Based on the Bayesian linear inverse theory, the simultaneous inversion for petrophysical and pore-connectivity parameters are achieved. To characterize the statistical variations within the lithofacies, the Gaussian mixture model is introduced to describe the prior distribution of the objective parameters. The analytical expression for the posterior distribution of the objective parameters is obtained with the linearized forward operator. Numerical tests indicate that the accuracy of predicted elastic parameters by the proposed method is improved compared with the conventional Xu-White model and the varying pore aspect ratio method. The application to the field data validates the effectiveness of the method, wherein the porosity and fluid saturation results help indicating the spatial distribution of potential reservoirs.