Late fuel during closing of the valve of a fuel injector and fuel films stuck on the wall around the nozzle outlets are sources of particulate matters (PM). In this study, we focused on the effects of the valve motions on the late fuel and the fuel films stuck on the walls around the nozzle outlets. We previously developed a particle/grid hybrid method: fuel flows within the flow paths of fuel injectors were simulated by a front capturing method, and liquid-column breakup at the nozzle outlets was mainly simulated by a particle method. The velocity at the inlet boundary of a fuel injector was controlled in order to affect the valve motions on the late-fuel behavior. The simulated late fuel broke up with surface tension around the time of zero-stroke position of the valve, then liquid columns and coarse droplets formed after the bounds of the valve, and finally only coarse droplets were left. We found that the late fuel was generated by low-speed fuel-flows through the nozzles during the bounds of the valve. The effect of the bounds of the valve on the fuel films stuck on the wall around the nozzle outlets was also studied with a simulation that removed the bounds of the valve. The volume of the fuel films stuck on the wall of the nozzle outlets decreased without the bounds of the valve.