A method is provided for determining the sequence of nucleotides on a single strand DNA molecule. The single strand DNA molecule is attached to a leader oligonucleotide and its complementary strand to a solid state support. Fluorescently-labeled 3'-blocked nucleotide triphosphates, with each of the bases A, G, C, T having a different fluorescent label, are mixed with the bound DNA molecule in the presence of DNA polymerase. The DNA polymerase causes selective addition of only the complementary labeled NTP, thus identifying the next unpaired base in the unknown DNA strand. The 3'-blocking group is then removed, setting the system up for the next NTP addition and so on. The sequence is repeated until no more fluorescently-labeled NTPs can be detected as being added by the polymerase.