In this paper, we consider the problem of robustly and accurately estimating the shape parameters of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -distributed sea clutter in the maritime radar industry. Outliers formed by non-sea-surface echoes have a significant negative impact on the estimation accuracy of the shape parameters. To improve the estimation accuracy, we first propose a bipercentiles feed forward network for the shape parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> (BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> ), which makes use of a ratio of two percentiles and a two-hidden-layer feed forward neural network. The BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> can learn the mathematical relationship between the shape parameter and the ratio of two percentiles, and can work in environments where the number of outliers is approximately known. In addition, to deal with the case where the number of outliers is not known due to dynamic changes in the environment, we also design another neural network (referred to as MBP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> ) which consists of multiple BP-FFNNs- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> and a multi-class classification network. The MBP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> can perceive the change in the proportion of outliers, so an accurate estimate of the shape parameter can be obtained from a BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> that is not affected by outliers. Finally, training and test data are constructed to train and evaluate the two proposed estimation methods, respectively. Experimental results demonstrate that the proposed BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> performs better than traditional moments-based estimators, and has almost the same performance as the tri-percentile estimator. Compared with the tri-percentile estimator, the BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> avoids frequent table lookups, and produces a continuous estimate. The proposed MBP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> can achieve more than 97% overall classification accuracy on simulated and measured data, and thus an accurate estimate of the shape parameter can be obtained when the number of outliers varies.