Coronal Mass Ejections (CMEs) are an important factor influencing space weather. To predict their arrival time at Earth and their geoeffective impact, accurate background solar wind simulations and three-dimensional reconstructions of CMEs are required. This paper selects a CME event that occurred on January 7, 2014. Using the steady-state mode of the Alfvén Wave Solar atmosphere Model (AWSoM), two background solar wind scenarios—incorporating the corona and inner heliosphere—were simulated based on GONG and ADAPT-GONG magnetograms, respectively. The three-dimensional velocity, density, pressure, and magnetic field of the CME were reconstructed using the Fitting of Gibson–Low (FGL) method, based on observations from three vantage points: SOHO, STEREO-A, and STEREO-B. The reconstructed three-dimensional CME was then inserted into the steady-state background corona, and the interplanetary propagation process of the CME from the corona to Earth was computed using the time-accurate mode of AWSoM. The errors between the CME arrival times at Earth calculated using the two background solar wind scenarios and the actual measured times were both within one hour, validating the effectiveness of the AWSoM+FGL approach.