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This letter deals with small target detection in passive millimeter wave (PMMW) imaging. Specifically, it focuses on a general detection scheme, where, first, the background is suppressed through a background prediction algorithm, and then the detection is accomplished. A precise prediction of the background is essential to a successful outcome. In practical applications, background estimation problem is more suitable to be considered as a nonlinear regression problem. Kernel methods are effective to solve the nonlinear problem. To improve the accuracy of the background prediction with kernel methods, we utilize robust loss function, to tolerate the noise outliers, and regularization methods, to avoid overfitting of the data. Experiments are conducted on PMMW images collected by a synthetic aperture imaging radiometer. The results demonstrate the effectiveness of the proposed algorithm.