Modern deep neural networks (DNNs) cannot be effectively used in mobile and embedded devices due to strict requirements for computational complexity, memory, and power consumption. The quantization of weights and feature maps (activations) is a popular approach to solve this problem. Training-aware quantization often shows excellent results but requires a full dataset, which is not always available. Post-training quantization methods, in turn, are applied without fine-tuning but still work well for many classes of tasks like classification, segmentation, and so on. However, they either imply a big overhead for quantization parameters (QPs) calculation at runtime (dynamic methods) or lead to an accuracy drop if pre-computed static QPs are used (static methods). Moreover, most inference frameworks don't support dynamic quantization. Thus we propose a novel quantization approach called QPP: quantization parameter prediction. With a small subset of a training dataset or unlabeled data from the same domain, we find the predictor that can accurately estimate QPs of activations given only the NN's input data. Such a predictor allows us to avoid complex calculation of precise values of QPs while maintaining the quality of the model. To illustrate our method's efficiency, we added QPP into two dynamic approaches: 1) Dense+Sparse quantization, where the predetermined percentage of activations are not quantized, 2) standard quantization with equal quantization steps. We provide experiments on a wide set of tasks including super-resolution, facial landmark, segmentation, and classification.