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The Viterbi algorithm can be realized by selecting the code sequence, which has a minimum Hamming distance through the trellis from the received sequence. In fact, the problem is similar to the well-known traveling salesman problem (TSP). Performing the Viterbi algorithm decoding of convolutional codes is shown to be equivalent to finding a global minimum of the energy function associated with a neural network. A neural network approach based on the mean field annealing (MFA) is presented to solve the Viterbi algorithm used in digital communication. The energy function required by the MFA is formulated. A computer simulation is given to demonstrate the effectiveness and validity of the proposed approach.