DNA Computing utilizes the properties of DNA for performing the computations. The computations include arithmetic and logical operations such as multiplication. We first show a procedure for multiplication of a pair of two binary numbers. The procedure mainly consist of bit-shift operation where the operation depends on bit position of one’s (ignoring zero’s) in the multiplicand and finally addition operations which take place simultaneously in each steps. The above method takes O(1) time in the best case which exists when each bit of multiplicand is zero. However, the time complexity of proposed algorithm is O(n) for average and worst case and the space complexity of proposed algorithm is O(n) for average case, worst case and best case. In addition the most merit of this model is simple coding and its time efficiency.