Understanding electron transfer in molecular systems is important, especially in the context of molecular electronics. With the desire to incorporate biological molecules in molecular electronic devices, there is a need to establish the relative importance of the various factors like the environment and the molecular structure (DNA sequence) on the electrical conduction. There has been much debate about mechanisms of electron transfer in biological molecules. We have conducted a systematic study of electron conduction across DNA molecular segments using the non-equilibrium Green function (NEGF) method. The Hamiltonian matrix elements were determined within the framework of the Extended Hückel Approximation. In considering (CG) base pair sequences, we find that the conductance decreases with segment length and that the substitution of (AT) base-pairs also reduces the conductance. When the DNA segments are in aqueous solution, the conductance is found to almost double in magnitude.