In the present article, we give a variant of the theory of gravity, which distinguishes between particles and antiparticles. In this theory that called two-signed gravity, in contrast to Einstein’s gravity, contributions from particles and antiparticles in the tensor, which are the source of the gravitational field are taken with different signs. In two-sign gravity, antiattraction exists between particles and antiparticles. In the framework of two-signed gravitation, it is naturally assume that Universe is not only electroneutral, but also gravitationally neutral too. In present paper, we suggest model of homogeneous, isotropic, uniformly expanding Universe. It is shown, what within framework of that model, which does not contain any free parameters, well explained observed dynamics of the Universe.