Sparse recovery (SR) is a promising tool for radar signal processing. However, SR-based target detection is still an open problem in the challenging scenarios of grid mismatch, very high dimensionality and constant false-alarm rate (CFAR) requirement. To address the above challenges, an efficient approach termed as knowledge-aided generalized approximate message passing (KA-GAMP) is proposed. Firstly, traditional signal processing (TSP) is performed to obtain prior knowledge about targets of interest. Based on this prior knowledge, dimensionality reduction is carried out, and a new approximate observation model of the received signal is established. Then, considering the grid-mismatch problem, target parameter estimations are carried out before SR, and an estimate of the measurement matrix is obtained. Finally, by exploiting the sparsity of the received signal, GAMP is adopted to perform target recovery. Based on recovery results, target detection is implemented. Interestingly, it is shown that the noise envelope outputted by GAMP approximately follows an i.i.d Gaussian distribution, and the proposed detector is CFAR. Numerical results via both Monte Carlo simulations and the measured data show that the proposed approach is superior to the TSP-based method in terms of target detection performance.