In recent years, social networking services such as facebook, twitter and some kind of blogs have been growing, obtaining more and more users and having larger impact on many areas of social activities. In these services, it has been noted that network externality plays an important role. The utility of a service depends on the number of users that use the service. In general, the growth curve of the number of the users etc. is nonlinear. So far, however, this nonlinearity has not been understood quantitatively. By applying the nearest neighboring agent model called Ising type agent model, we analyze the growth of a blog type social networking service. It is shown that the growth curve is quantitatively reproduced covering the whole range from the initial service-starting stage to the final saturating stage, despite the fact that the model has only two parameters. This means that the model is promising as a starting point of analyzing the growth and the impact of social networking services.