Neural networks converge faster with help from a smart batch selection strategy. In this regard, we propose Ada-Boundary, a novel and simple adaptive batch selection algorithm that constructs an effective mini-batch according to the learning progress of the model. Our key idea is to exploit confusing samples for which the model cannot predict labels with high confidence. Thus, samples near the current decision boundary are considered to be the most effective for expediting convergence. Taking advantage of this design, Ada-Boundary maintained its dominance for various degrees of training difficulty. We demonstrate the advantage of Ada-Boundary by extensive experimentation using CNNs with five benchmark data sets. Ada-Boundary was shown to produce a relative improvement in test errors by up to 31.80% compared with the baseline for a fixed wall-clock training time, thereby achieving a faster convergence speed.