Model-based integration algorithms are newly developed integration algorithms with unconditional stability and explicitness. A series of nonlinear time history analyses for a steel frame subjected to the earthquakes using a family of model-based integration algorithm were conducted so as to investigate the calculation process and the computing efficiency of the new algorithm. The stiffness-based beam-column element with fiber sections was used to simulate the steel frame and the model-based algorithm was adopted to solve the equation of motion for the structure. The detailed analytical procedure was provided. A four-story steel frame was designed in accordance with the American codes. A finite element numerical simulation platform was compiled with the aid of Matlab/Simulink. The finite element model of the steel frame was built accordingly. In the meantime, a finite element model of the steel frame using the OpenSees software was constructed as well. The Newmark constant average acceleration method was adopted to solve the OpenSees model, whose numerical results were used as references. The results show that when using the new algorithm, iteration is not required and satisfactory results can be obtained even if the integration time step is relatively large.