In the past few years since Adleman’s pioneering work on solving the HPP(Hamiltonian Path Problem) with a DNA-based computer [1], many algorithms have been designed on solving NP problems. Most of them are in the solution bases and need some error correction or tolerance technique in order to get good and correct results [3] [7] [9] [11] [21] [22]. The advantage of surface-based DNA computing technique, with very low error rate, has been shown many times [12] [18] [17] [20] over the solution based DNA computing, but this technique has not been widely used in the DNA computer algorithms design. This is mainly due to the restriction of the surface-based technique comparing with those methods using the DNA strands in solutions. In this paper, we introduce a surface-based DNA computing algorithm for solving a hard computation problem: expansion of symbolic determinants given their patterns of zero entries. This problem is well-known for its exponential difficulty. It is even more difficult than evaluating determinants whose entries are merely numerical [15]. We will show how this problem can be solved with the low error rate surface-based DNA computer using our naive algorithm.