RaptorQ code is a novel and efficient digital fountain code and its decoder is known to be too complicated. Considering the characteristic of the systematic code, a very fast decoding algorithm can be performed using matrix dimensionality reduction. The algorithm exploits a pre-calculated inverse matrix to achieve dimensionality reduction for the received code constraint matrix. As a result, the decoding complexity is reduced significantly while the failure-overhead curve is still identical to that of the conventional approaches. The simulations show that the decoding speed of the proposed algorithm outperforms the state-of-the-art algorithms, when the erasure probability of the channel is relatively low (less than 0.2).