Anticipatory postural adjustments (APA) generate initial center of mass motion during gait initiation and are associated with gait performance. While APA amplitude and duration have been linked to gait speed under single-task conditions, it remains unclear how these relationships are altered when motor control is constrained by cognitive demands. This study aimed to examine the association between APA characteristics prior to gait initiation and gait speed under dual-task conditions with externally paced cognitive load. Thirty-one healthy young adults performed fast walking under single- and dual-task conditions. Gait speed and APA parameters, and first-step range of motion were assessed using inertial measurement units. To examine associations between APA parameters and gait speed, multiple regression analyses were conducted separately for each condition. Longer APA duration was associated with decreased gait speed under both conditions. Greater anteroposterior amplitude of APA was associated with increased gait speed only under the dual-task condition, whereas no such association was observed under the single-task condition. No significant association was observed between cognitive performance and gait speed. These findings indicate that the association between APA characteristics and gait speed differs depending on task demands, suggesting that cognitive-motor constraints may modify the role of anticipatory control in gait performance.