Vehicular wireless networks have emerged as a promising wireless communication technology in recent years. Vehicular wireless networks collect information on real-time traffic, such as the road situation, the location of a car accident, etc., which must be delivered to its destination before a set deadline in order to be useful for an Intelligent Transportation System (ITS). Target applications are called safety-critical information. However, vehicular wireless communication does not incorporate reliable transmission of safety-critical information which will experience wireless errors due to collisions or the noisy environment caused by the high speed of moving vehicles. If the driver of a vehicle does not receive the information in time, this may cause a critical condition. This paper proposes a Reliable Transmission Mechanism (RTM) to solve this problem. The RTM relies on extra parity bytes adaptively added to a byte-level forward error correction mechanism to enhance the transmission quality of safety-critical information. This paper simulates the RTM and compares it with conventional vehicular wireless networks in terms of effective packet loss rate, retransmission count and average end-to-end delay. The simulation results show that our proposed RTM protects the information effectively.