Dispersion fuel is used in high-temperature reactors (HTRs) and some other advanced reactors. It contains a stochastic mixture of microsphere fuel grains or burnable poison grains embedded in a matrix material, which leads to the so-called double heterogeneity problem in the neutron transport calculation. This work investigates an equivalent homogenization method to deal with the stochastic media. In this method, the stochastic media are transformed to a homogenized material by introducing spatial self-shielding factors and preserving first-collision probabilities. A transmission model is proposed to calculate the first-collision probabilities and the self-shielding factors. In addition, the method is extended to treat the stochastic media with multitype grains. The applicability and correction techniques for the proposed method are discussed. The proposed method has been implemented in a lattice physics code named XPZ for HTRs. Numerical results are presented for typical HTR fuel pebbles and are validated against Monte Carlo solutions. It is concluded that the proposed equivalent homogenization method is promising for treating the double-heterogeneity problem and can be conveniently implemented in existing lattice physics codes.