The map projection problem involves transforming the graticule of meridians and parallels of a sphere onto a plane using a specified mathematical method according to certain conditions. Map projection transformations are a research field dealing with the method of transforming one kind of map projection coordinates to another. The conversion from geographical to plane coordinates is the normal practice in cartography, which is called forward transformation. The inverse transformation, which yields geographical coordinates from map coordinates, is a more recent development due to the need for transformation between different map projections, especially in Geographic Information Systems (GIS). The direct inverse equations for most of the map projections are already in existence, but for the projections, which have complex functions for forward transformation, defining the inverse projection is not easy. This paper describes an iteration algorithm to derive the inverse equations of the Winkel tripel projection using the Newton-Raphson iteration method.