Although single-leg squats are a common dynamic balance clinical assessment, little is known about the relationship between parameters that influence squat movement and postural control performance. The objective of this study was to determine the relationships between squat parameters (speed and depth) and postural control under single task and dual task. A total of 30 healthy college students performed single-leg squats under single task and dual task with Stroop. Random-intercepts generalized linear mixed models determined the effect of squat parameters on center of pressure (CoP) parameters. For each 1-cm·s−1 increase in squat speed, sway range (mediolateral: β = −0.03; anteroposterior: β = −0.05) and area (β = −0.25) decreased, whereas sway speed (mediolateral: β = 0.05; anteroposterior: β = 0.29; total: β = 0.29) increased. For each 1-cm increase in squat depth, sway range (mediolateral: β = 0.05; anteroposterior: β = 0.20) and area (β = 0.72) increased, whereas sway speed (anteroposterior: β = −0.14; total: β = −0.14) decreased. Compared with single task, the association between total and anteroposterior sway speed and squat speed was stronger under dual task. Clinicians and researchers should consider monitoring squat speed and depth when assessing dynamic balance during single-leg squats, as these parameters influence postural control, especially under dual task.