Sammon's nonlinear mapping (NLM) is an iterative procedure to project high dimensional data into low dimensional configurations. This paper discusses NLM using geodesic distances and proposes a mapping method GeoNLM. We compare its performance through experiments to the performances of NLM and Isomap. It is found that both GeoNLM and Isomap can unfold data manifolds better than NLM. GeoNLM outperforms Isomap when the short-circuit problem occurs in computing the neighborhood graph of data points. In turn, Isomap outperforms GeoNLM if the neighborhood graph is correctly constructed. These observations are discussed to reveal the features of geodesic distance estimation by graph distances.