This work presents a theoretical model to calculate the acoustic radiation force of a fluid cylindrical particle immersed in water near a boundary. A solution of the acoustic radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface area, is derived for a cylinder near a boundary in normal incident plane wave by applying the translation addition theorem of cylindrical function. The effects of impedance boundary on acoustic radiation force of a fluid oleic acid cylinder and a mixture fluid cylinder immersed in water are analyzed with particular emphasis on the radius of fluid cylinder and the distance from its center to the impedance boundary. The results reveal that the existence of particle trapping behavior depends on the choice of the nondimensional frequency ka as well as the offset distance from the impedance boundary. This study provides a theoretical basis for acoustic manipulation, which may be of benefit to the improvement and development of the acoustic control technology.