Existing deep convolutional neural network (CNN) architectures frequently rely upon batch normalization (BatchNorm) to effectively train the model. BatchNorm significantly improves model performance, but performs poorly with smaller batch sizes. To address this limitation, we propose kernel normalization and kernel normalized convolutional layers, and incorporate them into kernel normalized convolutional networks (KNConvNets) as the main building blocks. We implement KNConvNets corresponding to the state-of-the-art CNNs such as ResNet and DenseNet while forgoing BatchNorm layers. Through extensive experiments, we illustrate that KNConvNets consistently outperform their batch, group, and layer normalized counterparts in terms of both accuracy and convergence rate while maintaining competitive computational efficiency.