A variety of algorithms exist for optical single molecule tracking in two and three dimensions. One general class of algorithms employs cost-functionals to link the individual fluorescent spots, produced by a molecule in sequential video frames, into trajectories. This method has also been used to track one-dimensional (1D) molecular motions for relatively low diffusion rates (i.e., D < 1 μm(2)/s). At high diffusion rates, the cost-functional approach often fails to accurately reproduce 1D trajectories, particularly when the molecules are closely spaced. In this paper, we present a new algorithm called trajectory-profile-guided (TPG) tracking that is designed specifically for 1D trajectories. TPG tracking involves an initial search for one-dimensionally aligned fluorescent spots (i.e., candidate molecules). Qualifying candidates are subsequently identified and linked into trajectories based on several criteria. We test the TPG algorithm's accuracy and precision against cost-functional based tracking using both simulated and experimental video data. The results show that TPG tracking more accurately reproduces the actual 1D trajectories, particularly at higher diffusion rates. TPG tracking is also shown to produce longer trajectories and more accurate estimates of trajectory aspect ratios (i.e., their dimensionality), molecular diffusion coefficients, and order parameters for aligned 1D trajectories over a wide range of diffusion coefficients.