Objective: A model of quantum gravity unrelated to general relativity is described. The main postulate of the model is the assumption of the existence of a background of superstrongly interacting gravitons. To describe the interaction of a graviton with any particle during their collision, a new constant is introduced. Methods: It is shown that screening of the background of single gravitons by a pair of bodies leads to approximately equal attractive and repulsive forces between the bodies. Pairing of a part of the background gravitons, provided that the pairs are destroyed as a result of a collision with a body, yields an attractive force twice as great as the repulsive force, and gravity arises as an effect of background screening. Results: Newton’s constant has been calculated in the model as a function of background temperature, which allows the value of the new constant to be estimated. This model is free from divergences, unlike quantum gravity models based on general relativity, due to the specific shape of the Planck spectrum of the graviton background. A theoretical estimate of the Hubble constant, depending on the new constant, is also obtained. Conclusion: An important feature of the model is the necessity of an "atomic" structure of matter, which leads as a side effect to the prohibition of the existence of black holes that do not have such a structure. Small additional effects of the model, caused by the interaction of photons with gravitons, may have great significance for cosmology.