Binary feature representation methods have received increasing attention due to their high efficiency and great robustness to illumination variation. However, most of them are hand-designed feature descriptors that generally require much prior knowledge in their design. This paper introduces a Row-sparsity Binary Feature Learning (Rs-BFL) method to adaptively learn and encode palmprint features for open-set palmprint recognition. Given the training palmprint images, RsBFL jointly learns a bank of linear projection functions that transform the informative texture features into discriminative binary codes. Afterwards, we calculate the block-wise histograms of each feature map and concatenate them as the final feature representation. Based on the pre-trained projection matrix, we mapped the palmprint texture features of the test samples into binary features for matching. For RsBFL, we enforce three criteria: 1) the quantization error between the projected real-valued features and the binary features is minimized, at the same time, the projection noise is minimized; 2) the latent label semantic information is utilized to minimize the distance of the within-class samples and simultaneously maximize the distance of the between-class samples; 3) the l_{2,1} norm is used to make the projection matrix to extract more discriminative features. Extensive experimental results on two publicly accessible palmprint datasets demonstrated the effectiveness and powerful learning capability of the proposed method.