In goal-directed behavior, individuals are often required to plan and execute a movement with multiple competing reach targets simultaneously. The time constraint assigned to the target is an important factor that affect the initial movement planning, but the adjustments made to the starting behavior considering the time constraints specific to each target have not yet been clarified. The current study examined how humans adjusted their motor planning for double potential targets with independent time constraints under a go-before-you-know situation. The results revealed that the initial movements were modulated depending on the time constraints for potential targets. However, under tight time constraints, the performance in the double-target condition was lower than the single-target condition, which was a control condition implemented to estimate performance when one target is ignored. These results indicate that the initial movement for multiple potential targets with independent time constraints can be modified, but the planning is suboptimal.