In the future, 5G radio access and support for the internet of things (IoT) is becoming more important, which is called machine type communications. Different from current mobile communication systems, machine type communications generates relatively small packets. In order to support such small packets with high reliability, channel coding techniques are inevitable. One of the most effective channel codes in such conditions is the tail-biting convolutional code, since it is used in LTE systems due to its good performance for small packet sizes. By employing a list Viterbi algorithm for the tail-biting convolutional code, the block error rate (BLER) performances is further improved. Therefore, this paper evaluates the BLER performances of several list Viterbi algorithms, i.e., circular parallel list Viterbi algorithm (CPLVA), per stage CPLVA (PSCPLVA), and successive state and sequence estimation (SSSE). In the evaluation, computational complexity is also taken into account. It is shown that the performance of the CPLVA is better in the wide range of computational complexity defined in this paper.