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Introduction: the disease by non-alcoholic fatty liver is considered the hepatic expression of the metabolic syndrome and is accompanied by histological and functional alterations of the liver. The Morphometry is a valuable tool in the assessment of liver morphology. Objective: to describe the histomorphometric differences in the liver of a group of healthy rats and one of them subjected to a state of metabolic syndrome. Methods: a developmental, correlational, cross-sectional, experimental research study with quantitative approach was conducted in the period from October 2015 to September 2019, using a system of morphometric methods. Histological liver slices were analyzed to 16 male Sprague-Dawley rats randomly distributed in two experimental groups of eight animals for each group. Parametric test (one-factor ANOVA) was applied for group comparisons. The existing relationships between the variables were determined. Results: the area of the nucleus was greater in the hepatocytes of the perivenous zone in the induced group. The area of the cytoplasm was greater in the hepatocytes of the perivenous zone, but its behavior was homogeneous in the two study groups. Conclusions: the differences found between the control and induced groups with respect to nuclear and cytoplasmic area could constitute the morphological expression of the biochemical alterations caused by the metabolic syndrome. [ABSTRACT FROM AUTHOR]