A fully adaptive model order reduction scheme based on moment-matching is proposed to derive the reduced model of a linear time invariant system. According to the given error tolerance, the order of the reduced model, as well as the expansion points for the transfer function, are automatically determined on the fly during the process of model reduction. In this sense, the reduced model is automatically obtained without heuristically assigning the number of moments and expansion points before model reduction, which is a prerequisite for the standard implementation of model reduction based on moment matching. The proposed adaptive scheme is found to be efficient when it is tested on various linear time invariant systems.