Abstract: The conventional near-field millimeter-wave imaging from uniform sampling measurements does not work well in realizing real-time imaging due to high computational cost and long scan time. To this end, we present a near-field millimeter-wave imaging model from under-sampled measurements and the corresponding sensing matrix. Meanwhile, a fast millimeter-wave imaging algorithm based on generalized approximate message passing is proposed. The algorithm accelerates the convergence rate by embedding the generalized approximate message passing into the expectation maximization framework. In order to circumvent the construction and storage of large-scale observation matrix, we construct a fast implementation of the observation matrix using fast Fourier transform and wavelet filtering, which leads to an improved computing speed at the same time. Our experiments results confirm that the algorithm can reconstruct 2-D millimeter-wave images rapidly from under-sampled measurements, and it exhibits better performance in terms of both reconstruction quality and execution time compared with the fast iterative shrinkage-thresholding algorithm.