Glucose transporter 1 (GLUT1) is responsible for basal glucose uptake and is expressed in most tissues under normal conditions. GLUT1 mutations can cause early-onset absence epilepsy and myoclonus dystonia syndrome (MDS), with MDS potentially lethal. In this study, the effect of the R126C mutation, which is associated with MDS, on structural stability and substrate transport of GLUT1 was investigated. Various bioinformatics tools were used to predict the stability of GLUT1, revealing that the R126C mutation reduces the structural stability of GLUT1. Molecular dynamics (MD) simulations were used to further characterize the effect of the R126C mutation on GLUT1 structural stability. Based on the MD simulations, specific conformational changes and dominant motions of the GLUT1 mutant were characterized by Principal component analysis (PCA). The mutation disrupts hydrogen bonds between substrate-binding residues and glucose, thus likely reducing substrate affinity. The R126C mutation reduces the conformational stability of the protein, and fewer intramolecular hydrogen bonds were present in the mutated GLUT1 when compared with that of wild-type GLUT1. The mutation increased the free energy of glucose transport through GLUT1 significantly, especially at the mutation site, indicating that passage of glucose through the channel is hindered, and this mutant may even release cytoplasmic glucose. This study provides a detailed atomic-level explanation for the reduced structural stability and substrate transport capacity of a GLUT1 mutant. The results aid our understanding of the structure of GLUT1 and provide a framework for developing drugs to treat GLUT1-related diseases, such as MDS.