In the past decade, significant efforts have been made in developing physics‐based solar wind and coronal mass ejection (CME) models, which have been or are being transferred to national centers (e.g., SWPC, Community Coordinated Modeling Center) to enable space weather predictive capability. However, the input data coverage for space weather forecasting is extremely limited. One major limitation is the solar magnetic field measurements, which are used to specify the inner boundary conditions of the global magnetohydrodynamic (MHD) models. In this study, using the Alfvén wave solar model, we quantitatively assess the influence of the magnetic field map input (synoptic/diachronic vs. synchronic magnetic maps) on the global modeling of the solar wind and the CME‐driven shock in the 11 April 2013 solar energetic particle event. Our study shows that due to the inhomogeneous background solar wind and dynamical evolution of the CME, the CME‐driven shock parameters change significantly both spatially and temporally as the CME propagates through the heliosphere. The input magnetic map has a great impact on the shock connectivity and shock properties in the global MHD simulation. Therefore this study illustrates the importance of taking into account the model uncertainty due to the imperfect magnetic field measurements when using the model to provide space weather predictions.