Verifying robustness of neural networks given a specified threat model is a fundamental yet challenging task. While current verification methods mainly focus on the $\ell_p$-norm threat model of the input instances, robustness verification against semantic adversarial attacks inducing large $\ell_p$-norm perturbations, such as color shifting and lighting adjustment, are beyond their capacity. To bridge this gap, we propose \textit{Semantify-NN}, a model-agnostic and generic robustness verification approach against semantic perturbations for neural networks. By simply inserting our proposed \textit{semantic perturbation layers} (SP-layers) to the input layer of any given model, \textit{Semantify-NN} is model-agnostic, and any $\ell_p$-norm based verification tools can be used to verify the model robustness against semantic perturbations. We illustrate the principles of designing the SP-layers and provide examples including semantic perturbations to image classification in the space of hue, saturation, lightness, brightness, contrast and rotation, respectively. In addition, an efficient refinement technique is proposed to further significantly improve the semantic certificate. Experiments on various network architectures and different datasets demonstrate the superior verification performance of \textit{Semantify-NN} over $\ell_p$-norm-based verification frameworks that naively convert semantic perturbation to $\ell_p$-norm. The results show that \textit{Semantify-NN} can support robustness verification against a wide range of semantic perturbations. Code available https://github.com/JeetMo/Semantify-NN