This paper proposes a dynamic sliding mode control (SMC) approach to the robust voltage regulation of dc-dc boost converters by using interval type-2 fuzzy neural networks (IT2FNNs). First, uncertainties caused by the perturbation of the input inductor and the output capacitor are represented with some bounded approximation errors, by the utilization of a Takagi-Sugeno (T-S) fuzzy modeling approach. Based on the represented model of the boost converter, a new type of sliding surface is designed depending on the duty cycle and reference inputs of the converter. Then, a dynamic SMC law is designed, by considering that the perturbation of the uncertain parameters, including input inductor, output capacitor, load resistor, and input voltage, is bounded. Meanwhile, we adopt an exponential plus power approaching law in the sliding mode controller for fast reachability of the sliding surface and a small chattering in the duty cycle input. Moreover, in terms of the considered uncertainties, a novel IT2FNN-based dynamic SMC law is derived, by applying simplified ellipsoidal-type membership functions in the type-2 fuzzy neural network. To improve the capacity to manage the uncertainties, some online learning algorithms for the updating of the IT2FNN are designed by a gradient descent method (GDM), without the requirement of the boundedness of the uncertainties. The resulting tracking error system is synthesized to be bounded stable based on the designed IT2FNN-based dynamic SMC. Finally, the effectiveness of the proposed adaptive IT2FNN-based dynamic SMC method is verified by some comparative simulation results.