Sparse representation has received an increasing amount of interest in pattern classification due to its robustness. In this paper, a domain adaptation learning (DAL) approach is explored based on a sparsity preserving model, which assumes that each data point can be sparsely reconstructed. The proposed robust DAL algorithm, called sparse label propagation domain adaptation learning (SLPDAL), propagates the labels from labeled points in the source domain to the unlabeled dataset in the target domain using those sparsely reconstructed objects with sufficient smoothness. SLPDAL consists of three steps. First, it finds an optimal kernel space in which all samples from both source and target domains can be embedded by minimizing the mean discrepancy between these two domains. Then, it computes the best kernel sparse reconstructed coefficients for each data point in the kernel space by using l₁-norm minimization. Finally, it propagates the labels of source domain to the target domain by preserving the kernel sparse reconstructed coefficients. The paper also derives an easy way to extend SLPDAL to out-of-sample data and multiple kernel learning respectively. Promising experimental results have been obtained for several DAL problems such as face recognition, visual video detection and text classification tasks.