Disclosed are a method and apparatus for enabling a robot to follow an object by using distance measurement data and odometry data through ultra-wideband (UWB) to estimate a relative position of a target in a robot center coordinate system. The method comprises initializing a robot's own object following algorithm according to an object following request; transmitting a single-sided two-way ranging (SS-TWR) poll message; receiving a single response message in response to the SS-TWR poll message from the object, the single response message including second odometry information of a second odometry measurement device of the object; estimating a distance to the object based on a round trip delay calculated by an SS-TWR method; predicting a position of the object based on the second odometry information and first odometry information of the first odometry measurement device; and correcting the position of the object based on the estimated distance.