The cellular uptake of a particle through receptor-mediated endocytosis involves specific binding between ligands on the particle surface and diffusive receptors on the cell membrane. Since the rupture force of these specific bonds is generally random, the same can be the associated adhesion energy. To probe the effect of this randomness, we present a semistochastic model of receptor-mediated endocytosis, in which the adhesion energy between particle and membrane is regarded as a stochastic parameter obeying Boltzmann's distribution. It is shown that the so-called speed factor varies and that the rate of uptake is much lower than that from a previous deterministic model. It is also found that a spontaneous curvature can significantly increase the rate of uptake for particles of certain sizes. When constraining the random adhesion energy, we find that the rate of uptake can substantially increase. This work suggests that adhesion energy may be actively regulated during receptor-mediated endocytosis to improve the efficiency. By adopting random adhesion energy in the analysis, the physical picture of endocytosis implicated by the current work can be fundamentally different from that by a previous deterministic model.