Scale-invariant feature transform (SIFT) is one of the most robust and widely used local feature descriptor for image registration, however, the computational complexity of its key point descriptor computing stage is quite expensive and also the dimensionality of the key point feature vectors is relatively high. For speeding up the SIFT computation, a novel sparse random projection (SRP) based algorithm, namely SRP-SIFT, is proposed by combining SIFT with sparse feature representation methods from the compressive sensing theory. Accordingly, L1 norm is introduced to compute the similarity and dissimilarity between feature vectors used for image registration. The experimental results show that the proposed SRP-SIFT algorithm is much faster than the standard SIFT algorithm while the performance is favorably comparable when performing complex structured scene image registration applications.