In order to reduce the iterative decoding delay of convolutional turbo codes, this paper presents a concurrent decoding algorithm for the hardware implementation of turbo convolutional decoders. Different than a general turbo code, the hardware turbo decoder based on the proposed algorithm can update the priori information of message for each component code in a bit-by-bit manner as soon as it is generated by the other component code. The two component codes in a turbo code can thus be decoded concurrently, by using a single MAP decoder, subsequently reducing the decoding latency by approximately half while maintaining the bit error rate performance and a comparable hardware complexity, as a general turbo decoder.