Provided are a method for transmitting a message by a user equipment (UE) in a wireless communication, and an apparatus supporting the same. The method may include: initiating early data transmission; receiving a random access response message including an uplink grant, from a base station (BS); based on the uplink grant, determining whether or not to transmit a first message related to the early data transmission to the BS, in response to the random access response message; and after determining to transmit the first message related to the early data transmission, resuming radio bearers for the early data transmission.