The single-particle dynamics of a charged test particle in a background fluid under a magnetic field are studied using molecular-dynamics computer simulations. The off-diagonal as well as the diagonal components of the velocity autocorrelation functions (VAFs) are computed. The model interaction between the particles is a hard sphere. The diffusion constants and the Hall coefficients are also calculated at various densities. These are compared with a theory based on the projection-operator formalism. In the low density of a background fluid, the VAF can be well approximated by an exponential form. The Hall coefficients with respect to the volume fraction nu show a peak around nu =0.4, reflecting the fact that the ratio D/D_E should decrease to the value of unity from above where D_E is the Enskog diffusion constant.