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A new multi-group alcoholism model with public health education and alcoholism age is considered. The basic reproduction number $ R_{0} $ is defined and mathematical analyses show that dynamics of model are determined by the basic reproduction number. The alcohol-free equilibrium $ P_{0} $ of the model is globally asymptotically stable if $ R_{0}\leq1 $ while the alcohol-present equilibrium $ P^{*} $ of the model exists uniquely and is globally asymptotically stable if $ R_{0} \gt 1 $. The Lyapunov functionals for the globally asymptotically stable of the multi-group model are constructed by using the theory of non-negative matrices and a graph-theoretic approach. Meanwhile, the combined effects of the public health education and the alcoholism age on alcoholism dynamics are displayed. Our main results show that strengthening public health education and decreasing the age of the alcoholism are very helpful for the control of alcoholism.