The manipulation of particles by acoustic radiation force (ARF) has the advantages of non-invasiveness, high biocompatibility, and wide applicability. The study of acoustic radiation force is an important foundation for improving the accuracy and effectiveness of particle manipulation technology. Based on the acoustic wave theory, a theoretical model for the ARF of a free spherical particle in a bounded viscous fluid is established. The ARF for the case of a normal incident plane wave is derived by applying the translation addition theorem to spherical function. The dynamic equation of a free sphere is required as a correction term for calculating the ARF. The effects of the fluid viscosity, particle material, particle distance from boundary, and the boundary on the ARF are analyzed by numerical simulation. The results show that the resonance peak of the ARF curve is broadened with the increase of the viscosity of the fluid. Compared with the values of the ARFs of a PE sphere in a viscous and an ideal fluid, the fluid viscosity has a small influence and the viscosity effect can be ignored when kR is much less than 1. However, for the cases where kR is greater than or equal to 1, the amplitude of the ARF experienced by a particle in a viscous fluid is much greater than that in an ideal fluid. The influence of fluid viscosity on the ARF is significant and cannot be ignored. Moreover, compared with a liquid material sphere, the oscillation of ARF in an elastic material sphere is more pronounced. This is because the momentum transfer between sound waves and elastic materials is greater than that between sound waves and liquid materials. In addition, the amplitude of the ARF increases with the increase of the reflection coefficient of the impedance boundary, but its resonance frequency is not affected. Finally, the position of the sphere mainly affects the oscillation phenomenon of its ARF. The peaks and dips of the ARF become more densely packed with the growth of distance-to-radius. It is worth noting that the reflection coefficient mainly affects the amplitude of the ARF, while the position of the sphere affects the period of the ARF function. The results indicate that more efficient manipulation of particles can be achieved through appropriate parameter selection. This study provides a theoretical basis for acoustically manipulating a free particle in a bounded viscous fluid and contributes to the better utilization of ARF for particle manipulation in biomedical and other fields.