An error correction encoding and/or decoding apparatus and method of a digital dual-stream broadcast transmission and/or reception system. An error correction encoding apparatus includes a TRS encoding part to apply the transversal encoding to normal data packets and robust data packets and to append parity packets to the normal data packet and robust data packet, a randomization unit to randomize the data packets and the parity packets according to a predetermined pattern, an RS encoding unit to append parities to the randomized data packets and parity packets, a packet format unit to split the data packets and the parity packets into normal data and robust data and to process the normal and robust data, and a system control unit to control the packet format unit. Accordingly, a robust error correction encoding apparatus can be provided for the digital dual-stream broadcast transmission system to which Transversal Reed-Solomon (TRS) encoding is applied.