Double base number system (DBNS) is an alternative number system besides the binary system. Its representation is similar to the radix number system together with two bases, usually be two and three. DBNS preserves the two important properties: redundancy and sparseness. The redundancy is the property accommodating with the parallelism. In this research, we are interested in parallel addition algorithm on DBNS. Our theoretical result shows that parallel addition in DBNS can be performed. An addition algorithm together with the proof of correctness is described in this paper. In generally, we study the generalization form of DBNS addition algorithms in any sizes.