By the fractal dimension method, the polaron properties in cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowire are explored. In this study, the polaron effects in GaAs/Al_xGa_(1-x)As core-shell nanowire at different values of shell width and aluminum concentration are discussed. The polaron binding energy, polaron mass shift and fractal dimension parameter are numerically worked out each as a function of core radius. The calculation results show that the binding energy and mass shift of the polaron first increase and then decrease as the core radius increases, forming their corresponding maximum values for different aluminum concentrations at a given shell width. Polaron problems in the cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowire are solved simply by using the fractal dimension method to avoid complex and lengthy calculations. By the fractal dimension method, the polaron properties in cylindrical GaAs / Al x Ga 1-x As core-shell nanowire are explored. In this study, the polaron effects in GaAs / Al x Ga 1- (1-x) As core-shell nanowire at different values ​​of shell width and aluminum concentration are discussed. The polaron binding energy, polaron mass shift and fractal dimension parameter are numerically worked out each as a function of core radius. The calculation results show that the binding energy and mass shift of the polaron first increase and then decrease as the core radius increases, forming their corresponding maximum values ​​for different aluminum concentrations at a given shell width. Polaron problems in the cylindrical GaAs / Al_xGa_ (1-x) As core-shell nanowire are solved simply by using the fractal dimension method to avoid complex and lengthy calculations.