Road to a management career

I’ve been a network administrator for over 5 years and for the past year and a half, I’ve been involved in managing some projects, like VoIP conversion, developed relationships with vendors.

I have now the desire to land in a managerial position such as my boss’ position, IT director. I am very familiar with this position duties and requirements but because of lack of management experience I have not been considered/promoted. In fact, the position has been open twice, applied both, rejected once and now waiting on the second.

What do you suggest I start doing to begin a management career? education, training? I am also looking elsewhere since I don’t see any other opportunity with this company to advance.