An apparatus and a method for controlling a transmission of a vehicle are provided. The apparatus includes a determination device to determine whether to perform speed following control based on state information of a traffic light positioned on a road in front of the vehicle in coasting, a stop position predicting device to predict a stop position of the vehicle based on position information of the vehicle and the traffic light, a transmission stage decision device to determine a target position and a target speed based on the predicted stop position and to form a speed profile for each transmission stage to determine a final transmission stage based on the target position and the target speed, and a controller to perform speed following transmission control based on the final transmission stage.