Change-of-direction (CoD) ability is an important determinant of athletic performance. Muscle strength is among the most important determinants of CoD ability. However, previous studies investigating the relationship between CoD ability and muscle strength focused mostly on flexor and extensor muscle groups, or used multi-joint exercises, such as jumps, squats or mid-thigh pull. The purpose of the present study was to investigate the relationship between CoD ability and strength of ankle, knee, hip and trunk maximal and explosive strength. The participants (n = 327), consisting of male and female basketball players, tennis players and long-distance runners completed isometric strength assessments and CoD testing (90° and 180° turn tests). The times of both CoD tests were associated with muscle strength (peak torques and the rate of torque development variables), with correlation coefficients being mostly weak to moderate (r = 0.2–0.6). Strength variables explained 33%, 62% and 48% of the variance in the 90° turn task, and 42%, 36% and 59% of the variance in the 180° turn task, in basketball players, long-distance runners and tennis players, respectively. Hip and trunk muscle strength variables were the most prevalent in the regression models, especially hip adduction and abduction strength. Our results suggest that the strength of several lower limb muscles, in particular of the hip abductors and adductors, and trunk muscles, but also hip rotators, extensors and flexors, as well as knee and ankle flexors and extensors should be considered when aiming to improve CoD performance.