The sparse representation of signal via dictionary learning algorithms is widely used in signal processing field. Since there is redundancy in the new space defined by overcomplete dictionary atoms, the problem of finding sparse representations may bring the uncertainty and ambiguity in the presence of unknown amplitude perturbations, which is unfavorable to radar High Resolution Range Profile (HRRP) target recognition task. To deal with this issue, this paper proposes a novel algorithm called Stable Dictionary Learning (SDL), which constructs a robust loss function via marginalizing dropout to learn a stable adaptive dictionary. The algorithm considers the structure similarity among the adjacent HRRPs without scatterers’ motion through range cells, and enforces the constraints that the sparse representations of adjacent HRRPs should have the same supports. Moreover, SDL utilizes the structured sparse regularization learned in the training phase to automatically select the optimal sub-dictionary basis vectors, which is used for the classification of the test sample. Experimental results on measured radar HRRP dataset validate the effectiveness of the proposed method.