Abstract: Focusing on developing high accuracy gridless direction-of-arrival (DOA) estimation for low-bit quantized array, a fast gridless DOA estimation algorithm based on atomic norm minimization is proposed. Firstly the data fidelity between the low-bit quantized data and the unquantized data received at the array is established, and then the atomic norm minimization is applied to recover the DOAs. Thus the gridless DOA estimation problem can be transformed into the joint minimization of the mismatch between the quantized and unquantized measurements and the corresponding atomic norm defined by the received data. To efficiently solve the optimization problem, the accelerated proximal gradient technique is utilized, such that the solution can be iteratively updated by performing gradient descent with momentum and proximal projection. Compared with the classical subspace-based methods, the algorithm proposed in this paper is also applicable in the case of insufficient snapshots. Simulation results demonstrate the superiority of the proposed method both in accuracy and efficiency.