Mitochondria are eukaryotic organelles of bacterial origin where respiration takes place to produce cellular chemical energy. These reactions are catalyzed by the respiratory chain complexes located in the inner mitochondrial membrane. Notably, key components of the respiratory chain complexes are encoded on the mitochondrial chromosome and their expression relies on a dedicated mitochondrial translation machinery. Defects in the mitochondrial gene expression machinery lead to a variety of diseases in humans mostly affecting tissues with high energy demand such as the nervous system, the heart, or the muscles. The mitochondrial translation system has substantially diverged from its bacterial ancestor, including alterations in the mitoribosomal architecture, multiple changes to the set of translation factors and striking reductions in otherwise conserved tRNA elements. Although a number of structures of mitochondrial ribosomes from different species have been determined, our mechanistic understanding of the mitochondrial translation cycle remains largely unexplored. Here, we present two cryo-EM reconstructions of human mitochondrial elongation factor G1 bound to the mammalian mitochondrial ribosome at two different steps of the tRNA translocation reaction during translation elongation. Our structures explain the mechanism of tRNA and mRNA translocation on the mitoribosome, the regulation of mtEFG1 activity by the ribosomal GTPase-associated center, and the basis of decreased susceptibility of mtEFG1 to the commonly used antibiotic fusidic acid.