Sigmoidal curves, very common in epidemiology and biology, have traditionally been fitted using parametric models or fully non-parametric approaches like splines. In this paper, we propose a semi-parametric approach which is flexible enough to capture several sigmoidal shapes. The estimation procedure is iterative and relies on a first-order Taylor expansion around the inflection point. The performance of our approach is compared to some parametric models through a simulation study and an application to data. Results of simulations show that our approach performs well in terms of mean integrated squared errors in a variety of scenarios.