As artificial intelligence and deep learning models become increasingly sophisticated, processing vast amounts of personal data, the need for robust privacy protection measures has become paramount. This paper addresses the critical challenge of implementing privacy-preserving neural networks (PPNN) using fully homomorphic encryption (FHE), with a focus on the TFHE scheme. We present novel approaches to homomorphically implement maxpooling, a crucial non-linear operation in convolutional neural networks, which has been challenging to realize within existing FHE frameworks. Our main contributions include two innovative homomorphic maxpooling algorithms: HSMaxPool, utilizing the non-linear Sign function, and HRMaxPool, based on a homomorphic ReLU function. Both algorithms are implemented using TFHE’s gate bootstrapping and programmable bootstrapping techniques, respectively. Experiments were conducted on neural networks operating over ciphertext, employing the proposed homomorphic maxpooling algorithms. The results show that our methods deliver improved inference accuracy and reduced execution time compared to prior approaches, while maintaining accuracy throughout the maxpooling phase. This demonstrates the effectiveness of our homomorphic maxpooling algorithms in enhancing performance without sacrificing precision, further advancing the feasibility of efficient and privacy-preserving neural network computations on encrypted data.