The traditional semi-supervised sparse feature selection based on Laplacian graph has received extensive attention for its higher efficiency. However, due to the lack of extrapolation ability of the Laplacian operator, the limited labeled data is still not well utilized and is too sensitive for outliers. Therefore, an adaptive loss semi-supervised sparse feature selection algorithm based on Hessian regularization is proposed. Firstly, Hessian is used to preserve the local manifold structure of data in order to improve the linear mapping capability. At the same time, an adaptive loss function is exploited to measure the label fitness by adjusting the adaptive loss parameters, which significantly enhances model's robustness to data with a small or substantial loss. Moreover, $l_{2,p