The robustness of convolutional neural networks (CNNs) is vital to modern AI-driven systems. It can be quantified by formal verification by providing a certified lower bound, within which any perturbation does not alter the original input's classification result. It is challenging due to nonlinear components, such as MaxPool. At present, efficient and scalable verification methods are sound but incomplete, and thus, a certified lower bound is a crucial criterion for evaluating the performance of verification tools. In this paper, we present MaxLin, a robustness verifier for maxpool-based CNNs with tight linear approximation. By tightening the linear approximation of the MaxPool function, we can certify larger certified lower bounds of CNNs. We evaluate MaxLin with open-sourced benchmarks, including LeNet and networks trained on the MNIST, CIFAR-10, and Tiny ImageNet datasets. The results show that MaxLin outperforms state-of-the-art tools with up to 110.60% improvement regarding the certified lower bound and 5.13x speedup for the same neural networks.