There are many factors that appear to be directly related to the development of gambling addiction problems, and it is important to understand these relationships from a clinical perspective in order to develop prevention and intervention programs. Objectives This study seeks to analyze the relationships that gambling addiction has with gambling motives, cognitive distortions, and irresponsible gambling behavior, and proposes an explanatory model of this addiction. According to the model, enhancement acts as a predictor of cognitive distortions, which in turn predict gambling addiction, with irresponsible gambling as a mediator. Methods The sample was made up of 258 university students (59.5% women), with a mean age of 20.95 years (SD = 2.19). A series of questionnaires were applied to measure the variables involved, and bivariate correlations, simple and multiple linear regressions, and a structural equation model were analyzed. Results The results indicated that gambling motives were positively related to cognitive distortions, acting as predictors of these. Additionally, the proposed theoretical model showed goodness of fit on various indices and explained 69% of variance in cognitive distortions, 37% of that in irresponsible gambling, and 43% of that in gambling addiction. Limitations The main limitation of this research is that the sample belongs to a very specific population, who did not necessarily have gambling problems. Conclusions The main contributions are to uncover some of the relationships between gambling motives and cognitive distortions and to propose a mediating role of irresponsible gambling in the relationship between cognitive distortions and the development of gambling problems. If the proposed model is replicated, it may be of help to research and health professionals.