In order to explore the origin and physical nature of the ionosphere of Triton, a simple, 2-dimensional electron drift model is developed to approximate the ionization effect of magnetospheric electrons. The derived profile of ion production rate is then applied to a steady-state photochemical model calculation. It is shown that, as a result of the very low CH4 mixing ratio in Triton's atmosphere, the most dominant ion in the upper ionosphere could be N+. There are, however, difficulties in explaining the electron number density profile below 500 km as inferred from the radio science experiment on Voyager 2. One major factor is the increasing importance of the ion chemistry involving N+ and H2 from CH4 photolysis in this region. This problem may be partially resolved if we invoke a more efficient electron transport in the atmosphere or the possible presence of metallic ions like Si+, Ne+ and Na+ which do not react with N2 and H2 in the lower ionosphere.