Title: LAU: A novel two-parameter learnable Logmoid Activation Unit. Abstract: The activation function in deep neural networks has a major impact on the performance  of the training stage. In this work, we proposed a novel learnable Logmoid Activation  Unit (LAU), $f(x)=x\ln(1+\alpha \textrm{sigmoid}(\beta x))$, with two free parameters  $\alpha$ and $\beta$ that can be optimized via back-propagation algorithm. We design  quasi-interpolation type neural network operators with Logmoid-1 in a given feed-forward neural network for approximating any continuous function in closed spaces. This provides a theoretical basis for the excellent empirical performance of LAUs in experimental simulations. For instance, compared with ReLUs the proposed LAUs improves Top-1 classification accuracy on ImageNet-200 by $7\%$ respectively in ShuffleNet-V2, on CIFAR-10 by 6$\%$ respectively in EfficientNet-B0, and on CIFAR-100 by 5$\%$ respectively in MobileNet-V2. Our simulations show that end-to-end learning deep neural networks with learnable Logmoids can increase the predictive performance.