An adaptive Viterbi algorithm using strongly connected trellis decoding of binary convolutional codes is presented. It is known that the strongly connected trellis decoding method can be used to improve the efficiency of hardware utilization and the throughput of the decoding in a systolic array-based Viterbi decoder. However, this method makes the amount of ACS (addition, comparison, and selection) computations in the decoding process much larger than in the conventional trellis decoding. It is shown that the proposed adaptive Viterbi algorithm can reduce the large amount of ACS computations without a degradation in the performance. Further, this algorithm, unlike the adaptive Viterbi algorithm based on low connectivity trellis, does require a sorting operation to determine the most likely survivor paths among all the possible survivor paths. The simulation results show that the proposed adaptive Viterbi algorithm can reduce up to 70% of the average number of ACS computations per strongly connected stage over that using the conventional Viterbi algorithm, while keeping the same error performance as that of the latter.