The reconstruction of sunspot parameters in the early era of telescopic observations extends our knowledge on visual sunspot activity up to 400 years into the past. 200 digital solar images from 18 December 1610 to 28 January 1613 by the English astronomer Thomas Harriot were analyzed to yield sunspot counts, areas and positions. Harriot generally observed in the early morning when the Sun was near the horizon, and he specified the local time of observation, date, place, number of spots, zenith and ecliptic lines, and other information. We assigned 753 sunspots into 293 groups and defined their areas. We developed two approaches to reconstructing the heliographic coordinates of the sunspots. Method I makes use of the time of observation noted by Harriot, and Method II minimizes the day-to-day variability of sunspot latitudes independently of Harriot’s notes. The results of the two methods are discussed.