With regard to the increase of computing power in the past decades, finite element methods have been used to obtain the graphs of rotational moment curves which reflect non-linear effect in connections response. Several common semi-rigid connections are modeled and their behavioral properties are briefly reviewed, then the details related to a new semi-fixed connection have been provided. The behavioral properties like hardness, ultimate capacity and ductility are investigated and compared to other simulated connections. To perform non-linear analyses of connection, finite element software ABAQUS is used. In this simulation, it has been tried to have inter-component interactions according to reality as much as possible. Bolted connections are modeled exactly and the interaction among the bolt surface and hole is modeled as a hard friction with friction coefficient 0.3 with the ability of separating after loading. Also, fillet welds are modeled as a prism with triangular section. Where a groove weld is applied, since the strength in this type of welding is like base metal, two connection parts are stuck together. To mesh the element, C3D8R element is used. The proposed connection n1 has the most rigidity values among semi-rigid connections. Reducing the number of connection bolts has more reducing impact on connection rigidity value, so that with the half thickness of upper and lower sheets, rigidity rate is reduced only 9%, but with the half number of bolts, rigidity rate is reduced about 64%. Also the connection n3 have lowest rigidity rate and its rigidity amount is in the class of bolted connection in seat angle to web angle.