One of the methods to increase the ductility and energy dissipation of structures is the use of metal-elastomer dampers in the moment connections. In this paper, a new metal-elastomer damper is introduced and its seismic behavior under cyclic load is evaluate numerically. The damper studied in this research includes an elastomer layer to control slight vibrations and a number of yielding bolts to dissipate energy in strong earthquakes. In the new configuration, placing two dampers at the top and bottom of the beam is considered as an alternative to the formerly studied connections with one damper at the bottom of the beam. The effect of different parameters such as the number, diameter and height of the yielding bolts as well as the thickness of the elastomer layer has been studied and compared to the connection without damper. Numerical models are created in Abaqus software and validated using results from previous studies. Based on the results, the stiffness and strength of the connections with dampers having few yielding bolts is very small compared to the rigid connection (stiffness about 25% and strength about 40%). As the number and diameter of the bolts increase, stiffness and strength of the connection increase reaching the corresponding values for the original connection. However, the maximum plastic strain in connection decreases by more than 50% which is a sign of improved behaviour. It is worthy to note that plastic stains in bolts of connections with two dampers are less than that of connections with one damper.