I have developed an accelerated sparse time-invariant Radon transform (RT) in the mixed frequency-time domain based on iterative 2D model shrinkage in the time domain. I denote it as SRTIS. In the traditional sparse time-invariant RT in the mixed frequency-time domain, the sparse RT is modeled as a sparse inverse problem that is solved by the iteratively reweighted least-squares (IRLS) algorithm in the time domain, and the forward and inverse RTs are implemented in the frequency domain. In this method, IRLS is replaced by iterative 2D model shrinkage, i.e., the sparsity of the Radon model is promoted by some simple 2D model shrinkage operations in the time domain. Synthetic and real data demultiple examples using the parabolic RTs are given to demonstrate the better performance of the SRTIS when compared with the least-squares-based RT, the frequency domain sparse RT, and the traditional time-domain sparse RT in the mixed frequency-time domain.