An apparatus for controlling a transmission of a vehicle includes a processor configured to identify a location of a speed bump based on collected information about a specified section of a front road and determine whether the vehicle enters a section of the speed bump, and to set an oil pressure of the transmission to a first oil pressure in a normal driving section and set the oil pressure of the transmission to a second oil pressure when the vehicle enters the section of the speed bump, and a controller that controls the oil pressure of the transmission corresponding to a setting of the processor for each driving section of the vehicle.