Vehicle growth is a problem that is inseparable from sustainable transportation. In 2014, the number of private vehicle ownership in Indonesia reached more than 448 vehicles per 1,000 people. Specifically, for cars it reaches 324 vehicles per 1000 people. The growth of private vehicle ownership is strongly influenced by economic growth (one measure of the economic growth of the economy is Gross Domestic Product - GDP). It is necessary to look at the mathematical relationship between trends in economic growth represented by GDP and the growth of private vehicle ownership, with a model. This research is located on Java Island using provincial administrative based data (5 provinces namely Banten, Capital Region of Jakarta, West Java, Central Java, and East Java). The growth model of vehicle ownership on Java, in general, can be approached with the Gompertz Function. The Gompertz function is a type of mathematical model for a time series and is named after Benjamin Gompertz (1779-1865). It is a sigmoid function which describes growth as being slowed at the start and end of a given time period.