Most existing super-resolution imaging methods fail to work in low signal-to-noise ratio (SNR) condition due to the ill-posed antenna measurement matrix, but the sparse-truncated singular value decomposition (TSVD) method can effectively suppress noise and improve azimuth resolution in low SNR condition. However, the current sparse-TSVD method encounters large computation cost, resulting in a slow algorithm speed. In this work, a fast sparse-TSVD super-resolution imaging method of real aperture radar is proposed. First, the proposed method is based on the results of TSVD, using the truncated unitary matrix and diagonal matrix to reconstruct the signal convolution model. The dimension of the reconstructed antenna measurement matrix reduces from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times N$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \times N$ </tex-math></inline-formula> , and the dimension of the reconstructed echo matrix reduces from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times 1$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \times 1$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is azimuth sampling points and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is truncation parameter, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \gg k$ </tex-math></inline-formula> . Much of the expensive matrix– multiplication computation can then be performed on the smaller matrices, thereby accelerating the algorithm. Second, an objective function is established as the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l_{1}}$ </tex-math></inline-formula> constraint based on the regularization strategy. Lastly, this article employs iterative reweighted least square (IRLS) method to solve the objective function, and the dimension of the reversed matrix is lessened from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times N$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \times k$ </tex-math></inline-formula> , speeding up the algorithm further. The simulation and real data verify that the proposed algorithm not only improves the azimuth resolution in low SNR condition but also increases computational efficiency compared with the sparse-TSVD method.