DNA sequence alignment is an important tool for modern molecular biology. The algorithm used by many sequence alignment tools is the dynamic programming algorithm introduced by Needleman and Wunsch in 1970. This algorithm has a time complexity of O(n2), where n is the length of the input sequence. This dynamic programming algorithm has been implemented on a new parallel computing architecture called CellMatrix. CellMatrix is a computing architecture developed recently to take advantage of the extremely large number of atomic switches available through future nanotechnology. CellMatrix is a very good architecture for massive parallel computing. This implementation has achieved a time complexity of O(n) in finding the optimal alignment score for two DNA sequences.