The recently proposed Kolmogorov-Arnold Networks (KANs) offer enhanced interpretability and greater model expressiveness. However, KANs also present challenges related to privacy leakage during inference. Homomorphic encryption (HE) facilitates privacy-preserving inference for deep learning models, enabling resource-limited users to benefit from deep learning services while ensuring data security. Yet, the complex structure of KANs, incorporating nonlinear elements like the SiLU activation function and B-spline functions, renders existing privacy-preserving inference techniques inadequate. To address this issue, we propose an accurate and efficient privacy-preserving inference scheme tailored for KANs. Our approach introduces a task-specific polynomial approximation for the SiLU activation function, dynamically adjusting the approximation range to ensure high accuracy on real-world datasets. Additionally, we develop an efficient method for computing B-spline functions within the HE domain, leveraging techniques such as repeat packing, lazy combination, and comparison functions. We evaluate the effectiveness of our privacy-preserving KAN inference scheme on both symbolic formula evaluation and image classification. The experimental results show that our model achieves accuracy comparable to plaintext KANs across various datasets and outperforms plaintext MLPs. Additionally, on the CIFAR-10 dataset, our inference latency achieves over 7 times speedup compared to the naive method.