We propose an energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy Ec depends on the number of neighbors n of each site, but the various exponents do not. For n = 6, we got that Ec = 0.4545;and a self-similar structure of the energy distribution function with five major peaks is also observed. This is a natural result of system dynamics and the way the system is disturbed.