This study employs the concepts of complex networks to study the temporal dynamics of streamflow, with emphasis on annual scale (i.e., year-to-year connections). The study proposes a new approach to construct the streamflow network at the annual scale. It uses the daily streamflow data to construct the annual streamflow network, instead of using the annual (mean or accumulated) streamflow data. With this approach, each year serves as a node in the network, with each node having a time series of daily streamflow values (not a single streamflow value). Streamflow data observed over a period of 151 years (October 1862-September 2013) from the Mississippi River basin at St. Louis, Missouri, USA are considered for implementation of the approach. The properties of the annual streamflow network are investigated using three complex network-based methods: degree centrality, clustering coefficient, and degree distribution. The sensitivity of the results to streamflow correlation threshold is also examined. The results suggest that (1) there are only a few very significant nodes (years) in the annual streamflow network (degree centrality method); (2) the annual streamflow network is not a classical random graph, but may be a small-world network or scale-free network (clustering coefficient method); and (3) the network exhibits a combination of exponential and power-law distribution (degree distribution method). Based on the identification of a significant stretch of period (around the 1950s-1990s) with very weak connections with the rest of the period studied, the results also suggest the influence of dam construction (and other anthropogenic factors) on the evolution of annual streamflow dynamics.