With the nonlinear Schrodinger equation descripting of beam propagation in strongly nonlocal media, the interaction and propagation properties of (2+1)-dimensional hyperbolic-cosine Gaussian beams in strongly nonlocal nonlinear media are studied. The analytical expressions of propagation of hyperbolic-cosine Gaussian beams in strongly nonlocal nonlinear media and second moment beam width are obtained, while the interactions between two hyperbolic-cosine Gaussican beams are resolved and analysized numerically. The results show that when the incidence is a single beam, there exists a critical power. When the input power is equal to the critical power, the second moment beam width remains invariant on propagation, otherwise the second moment beam width varies with a period during propagation. When two hyperbolic-cosine Gaussian beams propagate together, they always attract each other, and the transverse intensity distribution becomes complicated. The on-axis intensity evolution and the intensity distributions of the interaction between two beams during propagation are discussed in detail.